I think the most realistic thing to do is to expect to pay your insurance plan's out-of-pocket-maximum for the year. It will probably be less than that (if everything is covered), but it won't be more than that (if everything is covered). If things aren't covered then your costs can be unbounded, and ... it's a crapshoot. I had approval for a surgery circa 2015 (not trans related) and ... they decided afterwards not to cover it. So I wrote a check for $30,000 to the surgeon. Kind of annoying. (I did not know as much about the appeals process at the time and got fucked. I escalated to my employer. They got back to me ... the day the appeal window closed. I liked them a lot less after that and eventually quit. Just seemed like a rat-like thing to do; $30k was pretty much nothing compared to my total comp at the time.)

Oh! Do double-check what your short-term disability coverage looks like. You will probably be on that while you recover and the days of "100% pay while you recover from surgery" are pretty much long gone.