[jerf]

I think you're looking for the "visual novel" genre.

By accidents of history, visual novel as a genre is strongly correlated with anime aesthetics and tends to focus on certain story genres that may or may not interest you. However, there's no fundamental reason for this, any more than there's a fundamental reason why "cartoons" in the US became strongly associated with "for children".

Quality is definitely also mixed, as the bar for entry of this style of thing is low. But that also means there's the sort of vibrancy and experimentation you get when there's virtually no "commercial market" functioning as a taste-maker by overwhelming all the smaller groups with big piles of money and raising the consumer's expectation of quality beyond what they can compete with.