KangaRube here: Theatre is probably a bigger direct influence than any VNs were. Starting in earnest around Covid lockdown era, I mostly was thinking of this kind of like a little play. Putting on a show with my friends. So I thought about Chekhov plays I had read or been to as a kind of reference on how to write, and thinking about what sort of actions could be added to dialogue to deepen subtext, and how blocking could affect it all. Even the design process for sprites can be a fair bit like directing actors.
So the writing of Chekhov, Shakespeare, and obviously also Aeschylus and Sophocles--- their handling of structure and character interactions had a lot of influence.
And from cinema, there is a lot to get from "mise-en-scene" directors and slow-cinema. Directors like Andrei Tarkovsky or Kenji Mizoguchi, who often stick to a single take for most of a scene, have an obvious connection to how most of a VN looks/acts. Those two above-mentioned directors have been a big inspiration and influence on what I try to bring to our paper doll play. Not to mention Cassavetes--- I have always thought there needed to be more of that kind of scruffy intensity in VNs, and still would like to aim to have that.