Oh, you're talking about 'Kanojo, Okarishimasu'! Honestly, the most common genre I see for them is slow-burn angst. A huge chunk of the fics revolve around the 'they finally confess and are together, but now they have to navigate actually being a real couple' scenario. Writers really dig into the emotional mess—Chizuru learning to be vulnerable, Kazuya dealing with his massive self-esteem issues, and them both struggling to move past the transactional start of their relationship. It's less about fluffy dates and more about therapy sessions disguised as romance.
That said, there's a surprising amount of 'what-if' AUs that ditch the whole rental girlfriend premise entirely. Coffee shop AUs are weirdly popular, maybe because it gives them a chance to meet on neutral ground. I've also seen a decent number of post-canon fics that imagine them years down the line, married with kids, which can be sweet but sometimes feel a bit too tidy considering the source material's chaos.
Crack fics exist too, where the joke is usually about Kazuya's inner monologue being audible to everyone, or Chizuru secretly being a yandere. Those are fun for a quick laugh, but the heart of the fandom really thrives on that prolonged, painful yearning.