Word usage quibble: A trans person’s “post-op gender” is the same as their pre-op gender; it’s their sex that has changed.
Short answer: According to the U S Bureau of Prisons (or at least according to this site who quotes them) if you’re post-op, you go to the side matching your new sex; if you’re pre-op, you stay in the side matching your birth sex. If you’re a trans woman and they’re pretty sure you’re not going to pass as a guy, they basically isolate you. You’ll probably get your hormones, but you won’t get your electrolysis or whatever prosthetics and underwear and such you’d prefer.
This brings up the question to me of classifying intersexed people who were classified as one at birth but prefer to live as the other-- since “pre-op” and “post-op” don’t always apply. But that’s another question.
The longer answer, of course, is “What qualifies as pre-op or post-op?” In Oklahoma, changing your legal gender is much like changing your name, except that you need to have your testes, or uterus and ovaries, removed at a minimum, and get letters from your therapist and whomever else you like, then go before a judge. (Note that in Oklahoma, you can be a man with a vagina, you just can’t menstruate out of it.)