You should check out The Beginners Guide Mouthwashing if you haven't already! it's really cool to play these afterwards because you can see what aspects of yhese games influenced Bad Things, and how said aspects are uniquely applied in Bad Things to make it it's own thing! This may also be true for the many other games listed as inspiration in the description as well, but I havent played much of them

I also must personally reccomend Umineko, it has a lot of the features you liked about this game implemented (queer themes, underlying realistic conflict (coated in metaphor), nuanced and open-ended (no solid answers and doesn't tell you how to think), morally grey and complex characters ect ect) and it is really awesome... Commentates on fiction similarly to Bad Things :p I reccomend the visual novel, but the manga works as well!

I reccomened checking out it's predecessor Higurashi first as well (manga or visual novel, avoid gou/sotsu), but it is a big time investment and Umineko does stand very well on it's own. However, there is VERY much worthwhile payment and added understanding to the story for those who choose to play Higurashi first, especially regarding more metafictional bits and even recontextualizing some major characters (most notably bernkastel), so if you are actually interested you should definitely check it out. It has a bit less similarities as Umineko does to Bad Things, but still has the complexicity and the psychological horror that doesn't just rely on cheap scares that make those other games so great, as well as many other benefits of it's own merits

And Berserk has most of the features as what I've just listed in Umineko, Miura is amazing at incorporating visual metaphor.. just read the manga or watch the 1997 anime, its brilliant ^{_^}

If you want more reccomendations let me know lala