Scientific Basis for Transgender ID

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I would really rather this thread not become a shitshow but this is unironically one of the few places I feel I will get a straightforward answer.

Very often I hear people of certain political persuasions describing self ID and gender dysmorphia as mainstream science. But I struggle to see how you could possibly ascertain whether someone with a penis and XY chromosomes has a "female brain". This seems like an untestable hypothesis to me, not least because there is no scientific definition of femininity/masculinity and our understanding of biological sex's relation to cognition appears to be in its infancy.

So my question is, what is the scientific basis for transgender women being women?