Here is an article about some basic pitfalls to avoid which may be helpful. There are also a few older threads on the subject which may be of interest too: here and here (although it seems that it ended up devolving into fights, there are likely some useful points of interest there too).
The most important thing, really, is that you want to treat the character with care and respect, so you’re coming at it from a good standpoint. The next important thing is to keep in mind that trans people aren’t a monolith and even if a lot of trans players feel you’ve got a character “right”, others will not - and it’s helpful to make peace with that. You are not going to be able to find a checklist that will make your work definite good “representation” unfortunately!
While there are common experiences, every trans character is going to be different - two trans women will look and be different to each other because they’re different people, let alone a trans woman and a trans man; some nonbinary people don’t see themselves as trans at all; people transition in different ways and with vsatly different feelings about their gender. All of which to say is, as with any character, it’s worth really getting to know your character, their personality, and how you’d describe them.
There are various trans youtubers who documented or discussed how they feel about their gender and transitions, and lots of memoirs from trans authors which may be helpful. I also suggest seeking out books and games about trans people, preferably created by them - this can be tricky sometimes because not all trans people are out - and exploring them. Around ten years ago there were loads of free Twine games made by trans people about their experiences, and you can find a lot of them archived on IFDB. There are plenty from more recent times as well, and there are a number of ChoiceScript games with trans characters - it is slowly becoming more common.
For a variety of reasons, I was nervous about writing binary trans characters, or going into more detail about nonbinary characters’ relationships with their gender, for a long time. When I was writing the trans characters in my new game, I took time to solidify and write down each character’s relationship with their gender, how it evolved over time, and so on. Then I did the same for the cis characters and their relationships with gender, masculinity, and femininity. It helped me understand the characters better and feel that they were more fleshed out. This may be helpful for you to do as an exercise.