Nope, you had it right the first time! Sasha is a trans woman who's had both top & bottom surgery (in Opportunity: A Sugar Baby Story, the game in which Sasha first appears, she's complimented by another trans woman on the work she's had done). The story isn't ABOUT Sasha being trans per se, but we did want to drop a fairly hard-to-miss reference to it right at the top.
Aha. I haven't played Opportunity yet, so I wasn't aware that she was in both.
The main part that had me confused was her disappointed response to Diogenes's mention that 'cross-species insemination is all but unheard of,' considering that as yet no trans women have had the capacity to get pregnant anyway, though maybe that's explained in Opportunity
That said, I do think she mostly reads as trans even without that, but I don't think I could tell you why.