Frustratingly few that I know of/can verify, and it may depend on exactly what you're looking for:
- Shield Highis the only one I've played extensively that meets those criteria fairly closely, but it's an old text-only RAGS game about strip-fights in a girls school, and the version here isn't the most up-to-date version anyway (there were also some forays into a bespoke engine but they seem to have fizzled out). I do think the writing is good enough on it's own to be worth a try, if you like writing alone though. That said, the content is pretty much all "do fight - have sex scene - queue up another fight - sex scene - etc" - other than one or two dates it's pretty barebones outside of that, but there's a fair few fights to find.
- KLK Ryûko's Rumble isn't out yet, but I'm keeping an eye on it because it seems like it's very similar to the above, but in a VN setting and with Kill La Kill characters.
- Femdom University / Fem U Zero are probably next-closest but I also think they were made with a male protag in mind and fem protag is a bit shoehorned in (at least, when I played the original, the female protag didn't even have a face). Have played a little of the first. Fetishes can be extreme at times.
- Kana Sensei looks like it counts, but is from the perspective of a dominant teacher than a student. Seems to be focused on spanking.
- Nex(e)us Institute is another where you play as a dom teacher; Not certain if it has any spanking (seems to be hypnotic mainly) but overview implies that you may end up as a sub yourself.
Overall, I don't think any of them quite have Missy's vibe, for lack of a better word. SH can go dom/sub but doesn't really have much life outside of the fights. FU/Z does have a bit more going on, but it pushes you hard into sub content. I expect KS/NI also has some more padding but with a push to dom content. But I also haven't played as much of some of them, so idk, could be wrong. I'd also like to know if there's more. As far as I'm aware, they don't really have the same feeling of being under an oppressive system but still being able to "win" in places.
(also I am waaaay behind in version as I stopped getting notifications for a bunch of threads, so I'm keen to see what's changed here that I missed over the last few months)