hey there! i'm a trans guy too so i can totally appreciate where you're coming from, but i think maybe the issue here is that the way the game begins, it does kind of feel like you're meant to be playing as yourself, what with how the mc has no memories and how you're asked to choose a name.............despite the fact that you really arent playing as yourself.
i mean maybe this is a little bit spoilery but the bit where you say "If my character already has a name and personality and stuff then them being a girl is fine".............the thing is that. is actually the case. but also this is a mystery game, and one aspect of this is that at the beginning you dont know the character's personality or backstory or anything (and only get a very brief glimpse of what she looks like). but she is her own character and when other characters use feminine language for her it isnt intended to be them gendering you and just assuming that you use fem terms, especially as the dev themselves uses they/them pronouns.
obviously being misgendered effin sucks and if playing the game just makes you feel misgendered or otherwise uncomfortable gender-wise then by all means don't play it, but it is a reaaaaaally good game that i love a lot so i wanted to try to clear this up, especially as you said that you were enjoying it to begin with. if it helps any, if you just hit enter when asked to put in a name, the game will automatically choose the name "valeria", which i think is meant to be the name she chooses in canon. (and there are easter eggs where if you enter the names of certain other characters you will get a certain reaction!) or you could maybe watch one of the walkthroughs/let's plays on youtube if you wanted.
also, even if you decide the game just isn't for you (which is completely fair), i cant help but also suggest checking out "therapy with dr albert krueger". it's set in the same world but with a main character who is very clearly their own character, and who uses they/them pronouns. i love it a lot!!!
but i hope this message came across ok (and i didnt seem dismissive or too pushy or anything), and that you have a good day :)