This is something I think about pretty regularly (see screenname,

), though I'm at a different point in my processing, I think, since I'm really settled on certain types of medical transition and very comfortable with what that will mean for my body. My current position on the "am I am man or a non-binary person" question is: it's impossible to say, and that's OK. Naming things can be tough for fluid/agender/nonbinary trans people, I think: I have a transmasculine friend on T who is dating a non-binary amab trans person. They have completely different relationships to masculinity, but they both put on eyeliner together before going out dancing. I don't think there's an easy category for either of them, but they sure are wonderful humans and I love the way they exist in the world.
Gender and sexuality are obviously very different things, but they definitely intersect when we talk about what counts as "masculinity" or "femininity" and what it means. There's a specific kind of socialization and gender presentation among myself/other trans friends who intersect with gay men in terms of community and orientation, but it's wildly difficult to define in these contexts, or decide how these categorize affect either the gender or orientation identities of everyone involved.
For instance: what's the difference between the kind of masculinity I share with most of my cis gay friends, and my own? How does a queer performance of masculinity intersect with genderfluid/gender variant identities? Gay men can clearly be cis, but perform their gender in the same way as a non-binary person. Am I a femme man or a non-binary transmasculine person? Is there a clear difference? My transfemme friends (who are not quite lesbian-identified but whose relationships most definitely resemble lesbian relationships far more than mine do) have real differences in terms of how their relationships work and who they find attractive/how they express their affection...but it's difficult to articulate and there are exceptions to literally everything here. There's a beautiful, varied array of possibilities in terms of gender, identity, and desire, and it's something I think our language isn't completely capable of capturing yet.
I want to masculinize my body as much as possible, because that's how I see myself--but I also want to play with how I perform my identity with that body, if that makes sense? I've sorta settled on being fine with being called a gay man, or a queer masculine person, a nonbinary trans man, a femme guy--each of these things misses a little something in who I am and who I love, but it's there in how I relate to other people and to my body. I use he and they interchangeably, and I really only feel badly misgendered if I get "she" or "ma'am."
In terms of gender therapy letters for transition services, it's easier to just say I'm a man and give "queer" or "gay" as my orientation if asked--it's not a date, and it's sometimes easier to simplify these things in clinical contexts. I'm lucky that I have access to a provider that doesn't consider sexual orientation when evaluating a trans person's need to access transition resources--I don't know if that's an issue for you, but it's good to be aware that some providers are really old school/discriminatory about nonbinary genders and/or sexual orientations.
^ sorry it's a bit long, I've had too much coffee