why pick one so fraught with emotion and controversy that will inevitably overshadow any debate?
The OP says:-
my intent here isn't to rehash the social or definitions-based debate on what gender identity is.
However this was a good pick, because...
If the consensus here is that first-person reports in this context are purely functional ("Easy Problem") or illusory, I’m interested in the specific epistemological criteria used to make that distinction without falling into physicalist reductionism.
In other threads discussing gender dysphoria, some posters have argued that that even if the feelings are genuine they are illusory. Ignoring the
fact that the brains of transgender people are shifted towards their gender identity, what logical reason is there to think that such thoughts cannot be real?
The common argument is that biology determines sex, end of story. If a person feels they are a different gender then they are simply deluded. However this implies that the mind's 'actual' gender is determined purely by sex, with no possibility of a variation between the brain and body. Problem is we don't know how the brain gets its gender identity, so how can we say that it
must match a person's sex? Unless we have proof of a mechanism that cannot fail, we can't make that determination, and have to accept the possibility that the feeling of being a different gender is 'real', ie. imprinted onto the brain at an early age just like cis gender is.
The OP asks:-
Is the subjective "felt sense" of gender strictly a functional output of neural architecture (an "Easy Problem" in principle)?
Yes. All thoughts are the result of neural output. If a person thinks they are trans gender it's because their brain's memories and 'wiring' are telling them that. "felt sense"
is neural output.
Or does the gap between third-person brain data and first-person subjective reporting highlight the limits of observational physicalism?
No. theoretically we could map the exact configuration of person's brain and so determine exactly what they are thinking. Only current technical constraints prevent us from 'reading minds'. We already have people with brain implants that directly 'read' (a small part of) their minds. In the future we may develop ways to 'see' the state of neurons associated with particular thoughts. To decode the data the subject could 'train' the mind reading device, perhaps using AI to recognize patterns and create a simulation of the mind in 'third-person' form.