A simple google search can yield some large results for those interested in the hypothalamus and how differentiated it is between what we call the genders. "Transsexual brains" results in about 206,000 hits. One of which: http😕/etransgender.com/viewtopic.php?f=10&t=510 is rather easy reading and does pretty much support all that Lisbeth has said.
Are there objections? Inevitably. Many, some just objections and some scientific that involve numbers and reliability, etc. But, it does seem that more and more researchers are discovering that identity has a physiological basis in the brain, the hypothalamus especially.
How I decide I'm going to read that is up to me. My decision is that my 'floating brain' would need some estrogen in its mixture in the tank.