I went and read the sequel and it opens with Kokuyou praying at a shrine to become a girl, getting upset that Shiro becomes a girl instead, and repeatedly states that they wish they were a girl throughout the currently translated 3 chapters.
You could probably point out that they refer to themselves as a boy when rejecting someone else but I take that more as a statement of “I’m a biological male, are you okay with that,” rather than just “I’m a boy.”
I dunno, it’s just how many times does a character need to say “I wish I was a girl” before we start questioning things anyways.
There are many reasons as to why someone would want to be a girl, one of them is gender dysphoria born out of Transsexuality, and I wouldn't judge those who read Kokuyou as such, but that isn't the only reason as to why someone would have those desires
As shown in the series, Kukoyou main wish is to be together with Kotarou, he can't do that while being a boy, because Koutarou isn't gay and others wouldn't accept his homosexuality. So Kukoyou, who's someone with a very different upbringing, lack of common sense, and is afflicted by depression and despair over the fact that their crush and best friend isn't able to be at their side anymore, decided to become a "girl", not in the sense of becoming a Woman in body, mind and soul, but in the sense of becoming a feminine figure, someone who can occupy the place given to women in society, that can perform the same actions and be perceived in the same way as them.
This isn't an uncommon fantasy, many homosexuals believe that life would be easier if they were the opposite gender, since this would allow them to be accepted and freely love those they want to love.
A character doesn't need to just want to be a girl to be trans, in my view, they need to have gender dysphoria or show a desire to change genders, for reasons unrelated to social expectations and/or the way they interact and want to be with others. You can question things, but I don't think it's right to cement that a character is trans and that this is the only possible view, just because they happen to interact with their gender in unusual ways.
Also, you have to remember that in the first chapters of the sequel is said two times that Kukoyou shouldn't become a girl for real, since this would kill his charm. So I don't think the work wants the audience to see Kukoyou as a girl or to want them to become one