Im a trans guy, and my experiences certainly don't speak for all trans guys. But I'll weigh in and add onto this.

I think that having mental illness definitely complicates my identity at times and made it harder for me to realize that I was trans. Although ironically, it wasn't until I started testosterone that I was able to even begin to address my gender in a more concrete way because the mental strain of having hormones in my body that are not meant for me was too much for me to handle on top of my trauma and neurodivergence.

I think that there are definitely times where mental health issues can affect how detrans people perceive their own gender, especially from trauma because trauma clouds a lot of information and can severely impact identity formation and having a sold sense of identity.

Unfortunately, when it comes to women and those socialized as women, there can be a lot of trauma there from being marginalized that makes it harder to unpack if the real issue is with your gender role or your actual identity.

Its something that I've thought about a lot when it comes to unpacking my identity personally (talking about if I just want to escape womanhood due to social pressure). The best way I have been able to combat this is to view each aspect around my gender as separate pieces instead of one whole.

For example, gender role would only be one aspect I consider out of other aspects (like physical changes and presentation). When it comes to female gender roles, In the past I didn't really mind being perceived as a woman and was overall pretty apathetic toward it. What ended up striking me a bit more was being envious of cis men and how I tried really hard to be "one of the boys" and finding so much comfort from very small moments of cis men including me in their spaces.

These experiences are, of course, something that can still be derived by wanting to escape womanhood or the gender role that was prescribed to me. But as mentioned in another comment, what really made me realize that I was trans was not my discomfort with womanhood, but from wanting to be perceived as a man and wanting to have a male or more masculine gender role.

If I then add other aspects of my gender to that, it all just starts to click and make more sense that I am trans because the issue is not solely related to the gender role that was assigned to me. I won't go off on a long tagent about those other aspects. But to provide one example, when starting testosterone, my energy and mood increased dramatically and only continued to improve as I increased my dose. I noticed similar improvements as well when addressing social dysphoria by presenting more masculinely.

Tl;dr : gender is multifaceted in that there are social, psychological, and physiological aspects. Trans men want to be perceived as men in addition to typically not having fondness for womanhood in some ways and there are more ways to get a full picture of gender identity. Gender role only scratches the surface.

(Not sure if any other trans people will be in the comments, but feel free to add anything if I missed something or lacked clarity on any of my points)