A couple points to get you started:

1. It isn’t really the case that said wards are specialising in the way you’re describing, but if they did, why wouldn’t you want (e.g.) all women (cis or trans) who are expecting their blood test results to reflect a certain balance range of hormones, or whose body fat locations and distributions are coded to be the same to be treated together? Especially after SRS, what benefit do you see from placing them in a “men’s” ward?
2. I understand you’ve drawn a distinction between “sex” and “gender” but “biological sex” isn’t binary, it’s bimodal, and although we don’t yet fully understand how it comes to be that people are gay or trans, there are a lot of compelling reasons to suggest that a lot of people may be trans for biological reasons. In which case, if you want to look at it from a diagnostic perspective, you’ll struggle to meaningfully define what “biologically female” means, and you’ll be more inclined to see it as “has had/not had high exposure to testosterone during formative years”. And as a trait, that can occur also to cis men and women alike, for multitudes of reasons. Biology just happens to be quite complicated, is all.