: How to write internally emotional characters? Over the past couple of days, I've asked questions about writing female characters with agency, and writing female characters as a male writer. Both

You are piling up fantasy on fantasy, so your characters and story look artificial

You basically took some characters from 21st century Western liberal world and made their lifestyle and ideas mainstream in 23rd century. You start the story with world in some kind of conflict (end of devastating war) but you never explain why your main characters live in relative luxury. If you start the story with the war and genetic modification, it is a biggest gun on your wall (Checkov's gun). You also do not explain why people in 23st century still go to taverns, catch the fish with nets, use boats with ropes etc ... To put it simply, your characters are two rich kids from 21st century transplanted to 23st century. And then, instead of further explaining 23rd century, you magically transport them to 14th century and start their adventure there.

My suggestion would be throw out unnecessary baggage. Either you are writing story about 14th century or 23rd. In former case, drop the introduction and make kids from current era somehow go to 14th century. Such kids would feel familiar to your audience, and you would not need to explain their behavior, social norms etc ... This would be easier path for you, because most of your story already belongs to 14th century. In latter case, well ... you would need to start anew and explain 23rd century.

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You are telegraphing what you as the author do not know, and this is killing any emotion and turning your story into a data-dump.

“I have no idea where we are or how we got here,” said Marko.

Sounds like you have not worked out the backstory.

Celeste looked at him blankly. “I clearly don’t know either. This is
beyond anything I have the toolkit for understanding.” She turned,
looking around the area, trying to find something… anything familiar.
She saw an olive grove in the distance, but didn’t remember it. Had it
been there before? She didn’t know. “Fuck!” she said.

Compare with: She saw an olive grove in the distance. Something about the color of the leaves, so like the fabric of her mother's skirt rustling as she pulled a tray of brioche from the oven. God, it had been years since she thought of that. Her father had loved Mere's brioche... her cooking... he used to joke that he married her for her mirepoix... and she'd hush him with a kiss and everyone knew it wasn't the sauce that kept them together.

Marko looked at her as if she were a stranger. “We may not know where
we are, but between the two of us we should be able to solve the
problem. We need to focus on what’s in front of us.”.

For all the world it sounds like you are trying to figure out the story as you are writing it.

"We may not know where we are, but we know we are from the same time. We know we have the same frame of the world." He was right, and it was a start. Like a recipe, like her mother would do. Start with the ingredients. A cup of flour, a teaspoon of salt... They had, at the very least, ingredients to start with.

She considered him and what he said. While she took a certain joy she
didn’t want to admit in teasing him about being young -- younger than
her by a whole four months -- he displayed a strength of character
that she hadn’t seen in others. And he was brilliant at problem
solving, which she saw in the way he played chess and go with his
father. Whatever this situation they were in, she felt safe with him.

Meh. (Thank God a strong man is there. /sarcasm.)

"His chess was passable, and he might even beat her at a match. But that wouldn't help them get back to their own time. Unless it was a matter of strategy. A matter of moves.

She was back in the study, with her father, and he said to her to always protect each piece with three other pieces. King, rook knight. Queen, pawn, bishop. Never move without a guard of three.

"We need a guard."

But what situation were they in? She had no idea. She felt sick to her
stomach. “I don’t even know how to describe what’s in front of us,
metaphorically speaking.

Dude, just figure it out. Assign what's going on. That's your job.

Clearly… well, okay, it seems that we’re on
the island we were on earlier today. Or yesterday. Or… I don’t know.
The island. It looks like the same one.”

“I agree. And this villa: it looks not-as-old as it did… earlier. It’s
like everything new is gone; like we’ve been thrown back in time.”

Time travel. Could she believe in it? Was it possible? She thought
back to her science professor talking about quantum physics, about how
scientists and mathematicians still only knew enough about it to know
we didn’t know enough, and he had been fairly certain nothing would
change. And there ended her learning about quantum physics and science
in general. At some point you had to realize that there were limits to
what you could understand, draw a line, and move on. And subjects like
business, economics, and politics were more to her interest than
unknowable science. Everyone, she told herself, had their limits. Her
stomach growled. “One thing I can say for sure, I’m hungry.

I bet you were hungry when you wrote that.

It sounds to me like your problem is you are discovery writing and trying to figure out what the hell is going on.

If you want emotion, there are tons of tips out there. Pull in what the characters' life experience is. Your job is to know it. That's part of worldbuildling.

Any detail can trigger anything. Any detail or memory or skill can be relevant. These are your tools.

Good luck.

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If I were to write this in my voice, there would be far less formality, less rationality, less insertion of background information. It would all be frantic dialogue and an occasional gesture.
OK, I'm going to write it in my own voice:

Marko looked left, right, out to the sea, each turn of the head a little faster than the last. “I have... I have no idea where we are. Or how we got here. I'm lost."
"Yeah." Celeste folded her arms, then unfolded them again. She had an urgent need to gesture. "Yeah. Unfamiliar. OK. So. OK. There's some explanation here."
"Hon, my first explanation is that I fell and hit my head and this is all a dream. In that scenario, you're not much help."
"Shut up. Not funny." She turned, looking around the area, trying to find something… anything familiar. She saw an olive grove in the distance, but didn’t remember it. Had it been there before? She didn’t know. “Fuck!” She grabbed his hand and squeezed it so hard she hurt her own fingers.
He returned the squeeze. That hurt, too. But it was a comforting reminder that he existed. "We'll be fine. We're both smart, remember? Let's sit down and take inventory."
"Inventory? What the fuck does inventory mean? We're on an island. It looks like the same island, except--redecorated."
"New drapes."
"Not funny. The stonework, that wall, it looks newer. Like somebody made a Hollywood set out of where we were before. If you mention Elizabeth Taylor or Errol Flynn I'm not going to warn you you're not funny; I'm going to hurt you."

I'm not carrying any load here but their frantic confusion, a tiny bit about the setting, and a tiny bit about how they interact while under stress. I feel that's all the situation can support.

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I agree, too much exposition. Which likely means, too little "setup" in your book.
If Celeste thinks Marko is brilliant at chess or Go, that should have been shown earlier, in the story setup. (ACT I, typically first 20% to 25% of the story.)
You are being too repetitive, you don't trust your reader or you have fallen into over-emphasis, saying the same thing multiple times in different words to make sure the reader "gets it". I've bolded some of what are effectively repetitions to convey the "I don't know" claim in this passage:

Celeste looked at him blankly. “I clearly don’t know either. This is beyond [me] anything I have the toolkit for understanding.” She turned, looking around the area, trying to find something… anything familiar. She saw an olive grove in the distance, but didn’t remember it. Had it been there before? She didn’t know. “Fuck!” she said.

Saying "I don't know" five times doesn't create the sense of disorientation I think you are looking for.
Here would be my first draft on your scene. Yours would be different, but to show you what I mean. I've made them more collaborative, as well.

They raced down the hill, dead even halfway but Marko pulled ahead. Then stopped short, in the middle of a meadow, looking into the distance.
"What happened?" Celeste said, a little breathless, pulling up to him.
Marko turned his head to look at her. “I have no idea where we are or how we got here.”
Celeste looked too, and realized he was right. She turned her gaze to her right. It felt vaguely familiar, but she couldn't quite recall where she had seen it.
“Fuuuuck!” she said, then took a deep breath and blew it out. "Me neither."
She flashed on why it was familiar. "The hills. They look the same as the island we were on yesterday. Right?" She was turning back to the left, and spotted something, pointing, "Look! That villa. Remember?"
Marko looked with her. "Yes! But it's new now. And the gardens are much larger. And not flowers anymore."
Celeste felt her pulse in her throat. "And there is no information booth, or parking lot. No paved roads, anywhere."
"Like we're back in time. That olive grove behind it is new, too."
That's impossible.
She put her hands to her head to feel for a holo viewer, but felt nothing. Her alarm rose, her breath still short. "It's a trick, Marko. That island is a hundred miles from here. This isn't real!"
"Don't panic," Marko said. He stepped to her, offering his hand palm up for her to take."We made a wrong turn, I think. It's real, but a set for a holo game or something."
She took his hand, and squeezed it hard for a moment, then took a deep breath. "Those are all simulations."
"Okay," he said, nodding. "A resort re-creation? A replica made by robots. Let's go see what this villa is about."
That's level headed. He's right. Gather evidence. Solve the problem.
She felt slightly embarrassed, she had been silly. The villa was the only evidence of humans in sight. She firmed her grip on Marko's hand and stepped forward, resolute. He responded in kind.
"If this is a replica it must have cost a fortune," she said. "I hope they have a restaurant."

Hopefully that helps. I left out the exposition, invented some stuff. And mine is longer, I think, with less information conveyed than yours. The point is instead of telling us all about Marko and Celeste, we reveal them slowly, all through their actions and dialogue. Readers don't mind learning what they need to know as they need to know it, and it is easier to remember if it happened in a scene.
The reason exposition usually doesn't work is because you are asking us to memorize dry facts and history, and we (readers) just cannot.
But we can remember a visualized scene and character actions (including feelings conveyed as part of the scene). This takes longer, but readers don't mind reading if a scene and interactions are in progress.
The Hollywood maxim is, 'Dialogue IS action'. Dialogue should always have an element of conflict in it, even if it is slight disagreement, even if that disagreement is only expressed in thought. It can also be surprise at something somebody said, confusion, resentment, anger, pity, etc. But preferably not just a long talk where everything is in agreement. It should also involve some stage craft, characters are moving, thinking, itchy people!
And although it is tempting to think of them serially (Marko says something, then Celeste says something, then Marko considers that and replies), IRL while you are talking I am thinking and half ignoring you, and vice versa. Think, what is Marko thinking about when Celeste is talking, and vice versa? It isn't always a volley, the same person can speak twice in a row, and the response to a statement may have nothing to do with the statement, the respondent's mind may have gone off on another track. That will come to you naturally if you stop to consider whether that happened or not.
Finally, your virtual acceptance of time travel is too quick. We don't believe impossible things until we are forced into it, and people from C23 will have sophisticated, immersive entertainment that will make them think of many things before actual time travel. They need to exhaust every possible other explanation first. It may take a serious injury or death before they accept that what they are seeing is real, and not acted. Hence the "resort for the rich" idea, a futuristic Disneyland, and the get it, nobody breaks character, ever, because it would cost them their job.
Of course, even in Disneyland, Goofy will break character if a man is disemboweled and dies in front of him. When something like that happens and none of the "actors" break character, and Celeste doesn't believe it was some kind of illusion, then she believes it's real. They time traveled.

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They are both being very detached and clinical about their situation. Perhaps that is a result of who they are and how they were trained, combined with a lack of serious challenge in their smooth as glass lives.

She seems to initially give up, turning into a damsel for him to rescue. ‘I don’t have the toolkit’ etc.

The villa possibly was not built yet,though one issue is that in that span of time there would be considerable differences in the appearance of the landscape, forests where in the future there are fields, vice versa.

Those first moments of shock could be silent, simply Celeste pointing at trees that ought not be there and wondering where or when they are. Once they determine the where, when becomes the X factor.

Get inside their heads. Imagine yourself waking up in a cave with a Rip Van Winkle effect and wondering ____________? You turn to your companion and do you say anything? If so, what and why?

The point made about dialogue going in directions otherwise intended is an excellent point.

Marko’s confidence that they can figure it all out might be sheer bravado.

These two have had a placid existence and such is not always conducive to complexity, but now they are many centuries in the past. The language, which should be the same, has altered over time and seems foreign to them.

Celeste gets to meet who she really is, discover what matters most to her. Her ambitions, fears and petty dislikes; everything that contributes to making her her.

Marko is also meeting his true self and discovering that he is both stronger and weaker than he thought and fear, such a foreign concept to them that they never really internalized the concept, becomes a part of their lives and they find courage.

Having these people a bit flat might work if you just want them as plot devices with names, but they can be dynamic.

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I will present the counter-point argument.

It's not you, these characters are just emotionally boring – and that's ok but focus on what's interesting instead.

Here's the problem. When I hear inside their heads they are distractingly someplace else, talking about something I don't care about (chess, some old professor). As a reader, I've already accepted that we have time-travelled so these people need to get up and start exploring (adventure) this world (wonder, milieu) or have a conflict (relationship, character arc) or start solving this puzzle (mystery) about time travel (idea, event). The story needs to start going in a direction so these narrative elements can begin to develop.

Instead these characters are feeding me expository backstory that doesn't seem very important to the current situation.

Their thoughts are not that interesting – they are stupefied by the sudden situation, but they are not having any emotional reaction, at least nothing I can identify. They are also not puzzle-solving through reason. I don't need to be this close to their minds. This meandering, disengaged internal monolog is pulling me out of the immediate situation which I am curious about.

It's ok that this is their reaction, it tells me something about who these people are and maybe their competency level. They are not panicking or blaming each other. They each seem to be cool-headed, or maybe it is caution or denial. Either way their reaction might change as they learn more about their situation, but I could grasp their emotional state in a few lines of dialog while the narrator stays focused on the world details, and that seems much more important right now.

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The problem I see with your writing, the answer to your question, is that you need to immerse yourself in your character's emotion. Put yourself in that emotional experience, in that moment. What do you feel? Your thoughts? Your responses? Your associations? Your visceral desires?

To use your example, having just time-travelled, Celeste is supposed to be confused, with a beginning of fear, right? Imagine yourself confused and scared. Would you, in that moment, wish to tease your companion about their age? Or would you want to grab their hand for support? Would you be all analytical about where you saw proof that the person next to you is good at problem solving, or would it just be a fact to you? At most, I think, you might remember a previous frightening episode the person got you out of - not strategy games.

Your character's internal monologue, her thoughts, are calm and analytical where we'd expect her to experience some emotion. Which makes a reader wonder if she is capable of experiencing emotions. You haven't gone deep enough into how she feels, and so you've created a disconnect between what we'd expect Celeste to feel, and what she displays.

I've actually struggled with a similar problem. I had this argument between a father and son written out. The comment of the first friend who read it was "yeh, that's how the father wishes the argument would have gone. Only he was angry, and afraid for his son, and a bunch of other emotions besides, so he ended up saying something completely different. And the boy was equally emotional about the whole thing, so his response wasn't what he would have liked it to be either. Now go and write not what they wished they had said, but what they actually said." After which I went and rewrote the scene with more visceral emotions and responses in it, and what do you know - it came alive.

To sum up, every time your character is supposed to experience an emotion, let them feel it. Not think "I'm afraid", but be afraid. Act afraid. Respond to being afraid. If you're still struggling, try to evoke the emotion within yourself. Feel that fear, not in your mind, but viscerally, and observe yourself in that state.

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