Studies don't show 'trans brains are more like the gender the person identifies with'. All of the studies that purport to show this, as far as I am aware, fail to control for sexual orientation of participants (these studies are typically done with those who have the early-onset type of dysphoria, and are disproportionately like to be same-sex attracted).
See
critique by Cantor here.
When sexual orientation is controlled for, the only difference that appears to be consistently associated with transgender identity is in the networks related to self and body perception. For example, in this study:
Structural connections in the brain in relation to gender identity and sexual orientation
"Several previous neuro-imaging studies have suggested that sexual differentiation of the brain is less pronounced in transgender individuals12,13,14,15, but none did specifically investigate sex, gender identity and sexual orientation in the same setting, directly comparing transgender groups with both cisgender homosexual and heterosexual controls. We found a significant main effect of Sex in several major white matter tracts (with higher FA in males), but, notably, not for Sexual orientation. Furthermore, congruent with our primary hypothesis there was a significant effect of Gender identity in the right IFOF. In the other tracts measured, the present study revealed, like in several previous studies, sex-atypical FA values in transgender individuals.
However, and importantly, these values became sex-typical after accounting for sexual orientation."
This has now been replicated several times in very recent studies. I don't have time to find all the links now, but some have probably been posted already although there was one that came out just a week or two ago.
This doesn't mean that these brain difference cause gender dysphoria since brain states are simply correlates.