: As a writer, how can I avoid exposing myself as a non-native English speaker in my texts? I am a Japanese student learning English, and one of my current goals is to learn to write texts

The writing in your question already sounds like a native speaker to me, so you're well on your way. Some areas to practice:

Find out what weaknesses people with your native language tend to have. In addition to prepositions, Mandarin speakers tend to struggle with verb tenses. Hindi speakers tend to use "reach" to mean "arrive". I don't know what mistakes are common for Japanese speakers, but English speakers in Japan probably do.
Read the style guide. You mentioned in the comments that you are interested in writing jobs. Almost every organization that employs writers has a style guide. The rules aren't always intuitive, even to native speakers. US newspapers have variations, but most are based off the AP Stylebook. It contains everything from the proper American spelling of words to when to use "black" instead of "African-American" to the proper term for a Mormon church. Newspapers also have their own paragraph style called the inverted pyramid. Academics, board-game publishers, scriptwriters, etc will all have different style guides.
If you use a thesaurus or translator, look up the definition of the word you choose. Young native English speakers also go through a phase where they choose random words to replace with fancier words from a thesaurus. They don't yet realize that every word has a slightly different meaning. Using thesauri and Japanese-English dictionaries when you think a more precise word would be useful is great, you simply need to check the resulting word means what you want it to.
Practice writing five-paragraph essays. You mention that native speakers tend to have strong topic sentences. A student in the US will probably write 50+ five-paragraph essays over the course of their education. College teachers complain about the five-paragraph essay all the time, but I would think of it like having a basis in Newtonian physics before learning relativity.
Read memes, puns, and authors known for word-play. The Series of Unfortunate Events by Lemony Snicket is a children's series that makes great use of word-play. Poets may be a good resource as well. These authors will show you how far you can stretch the English language.
Take risks. You'll learn faster if you're willing to make mistakes. Find a trusted native speaker or an anonymous online forum and try writing jokes or puns. Experiment with more convuluted sentence structure. Ask for feedback and explanations if something confuses you. This will allow you to make the leap from copying English writers to being a great English writer yourself.

Honestly, I find that non-native speakers tend to structure their writing more precisely than native speakers. Most of us native speakers are lazy. Most of us also aren't professional writers, and there are also professional writers of English for whom English is known to be a second language. There are poets who sprinkle their writing with native Spanish and novelists who write about their life growing up in the Middle East. Bilingual journalist is even its own job category on hiring sites.

In any case, best of luck.

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First, what you have written is very good, similar to (and honestly, better than) I've seen coming from native speakers of the language. That said, there are some ways you could have tweaked what you've written to have made it seem more natural.

Some examples:

and one of my current goals is to learn to write texts in such a way
that no reader will realize I am not a native speaker.

...and one of my current goals is to write in such a way that no one will realize I'm not a native speaker.

Here, for instance, a native writer would rely more on context. Saying "texts" and "readers" is redundant; if you're discussing writing, by default you're talking about writing text. If you were talking about poetry or song lyrics or advertising copy, something other than what we'd refer to as "text", then you'd specify it. Similarly, since you're talking about writing, you don't have to use "readers" in reference to other people. You're communicating via writing, by definition (unless they're using text-to-speech software) the others you're communicating with must be readers.

but the focus of my question is on avoiding exposing myself as a
non-native speaker rather than on merely writing good.

...rather than merely writing well. That's a simple grammar mistake.

which are my Achilles heel at the moment

...which is my Achilles' heel at the moment (or Achilles's, opinions differ). In any event, simple grammar error.

To write like native speakers, I strive to recall and use expressions seen or heard by me before rather than to construct my own expressions.

What you've written isn't wrong by any means, but it comes across as somewhat stilted. Someone writing in a more natural style would probably say have written something like:

To write like native speakers, I try to remember and use expressions I've seen or heard before rather than construct my own.

Word choice. Many non-native speakers either always use very simple
words or sometimes make weird word choices, choosing rare words for no
reason.

Amusingly, you've nailed it here: using "weird" is something a native speaker is likely to do. In a more formal style, someone might use "unusual" or "strange", but using "weird", at least in my dialect of English, comes across as very natural.

That aside, something that would alert me is not using contractions.

I am a Japanese student learning English, and one of my current goals
is to learn to write texts in such a way that no reader will realize I
am not a native speaker. I am humbly seeking advice on how to reach
that end.

To clarify, I do not intend to become a great writer...

...and grammatical constructions that I am sure about.

I would be grateful...

Not using I'm, I don't, and I'd would make me wonder. Even in formal settings, using I am constantly would stand out.

As to how to improve, and since you are specifically talking about writing rather than speaking, I'd say read a lot, fiction and non-fiction, but most importantly read contemporary material. Writing styles can change significantly over time, and if you don't want to seem anomalous now, you need to read what is being written in recent years, not something from decades past. Bontë and Austen and Dickens wrote very well, as obvious examples, but no one would write like that now.

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It's going to take time to know English to the point that it's going to be unmistakable from native English. I would suggest exposing yourself to the language, and soon, the average reader won't be able to tell the difference.

It's honestly just practicing English until others can't tell.

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For your point #3 (Style and structure) I found that essay writing is a very important part of "English speaking" curriculum, while in other countries it may be neglected (particularly if your major is not in humanities).

Obvious answer here is a lot of practice. You can benefit a lot if your can take an English writing class where your teacher will review your essays and suggest a number of improvements. At some point in the past, I considered myself already fluent in English (i.e. had sufficient vocabulary and grammar knowledge), yet writing even a simple essay was a very daunting task. With more practice, this had become easier, though I'm still not quite at the level of a college educated native speaker.

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There are only two ways to accomplish this:

Listen to and read LOTS of English to grow accustomed to how we say things. Can take years to reach the goal of being undetectable, but it won’t take nearly as long to get to where the average reader doesn’t notice.
Get a native speaker who is both a good writer and has linguistic training to help you edit what you’re writing.

But like someone else already said, if your writing is comprehensible, don’t worry about it.

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