And you will find a lot of them who will describe trying to be a man as the performance.One can make a case that even if they feel forced into it, they're still enshrining those stereotypes. Practically speaking , I can't see anyway to tell which males are attracted to these stereotypes (due to a paraphilia) and which feel compelled to conform to them (i.e. due gender dysphoria). In some it may be a mixture.
That being said, if you spend some time checking what TRAs post on Twitter, it seems pretty clear that are a fair amount that effectively do think that being a woman is a performance - in fact some claim that they are better at it (being women) than "cis-women".
Given that there is no "wears dresses and makeup gene," we all wear costumes and adapt behaviors to present the image we want to project to the outside world. Even if we don't think about it a lot. I'll submit myself as evidence. Intellectually, I suspect that a skirt/robe/or dress would actually be more comfortable in some weather conditions. However, I'm not going to wear one in public largely because it doesn't fit the acceptable costumes for my gender and I don't want to be seen as something I'm not. Were I in another culture or a Pope or Cardinal, I would have that option. But it's not available to me.
I don't like the word performance because it implies some sort of pretend, make believe, dishonesty or deception. When I perform the role of man, it is none of those, because that's how I identify. When a trans person performs a gender role that doesn't match their sex, they are also not pretending or being dishonest because they are performing the role that matches their gender, even if it doesn't match their sex.
The fact that it doesn't match their sex, however, necessitates a preference for the areas of gender presentation that do not overlap if they want people to react to them as the correct gender.
None of this, however relates to who gets into which spaces or who can compete in which sports leagues. That's because when those determinations are made it's not just about the individual, it relates to interaction with or perception by others depending on the setting or context.
Which is another reason I see no need for making arguments challenging the legitimacy of someone's identity. Everyone's identity is valid. But internal identity is not the only thing that dictates how a person interacts with society.