After thinking about it for a minute, I think the problem is me. Do you remember the scene from Matrix, where Cypher and Neo talk while looking at code? Cypher says how he sees blonde, brunette, and redhead, while everything Neo can see is code. I used to be Cypher, now I'm Neo. All I can see is tropes, tricks, and writing tools. Luckily, not all the time.
Like even the most mundane anime nowadays have a high chance of turning into a formulaic edgy competition for the plot to progress and to project 'meaning' to readers.
Hmm... I still like OPM. As for anime, I don't watch anime. But there is manga without edgy elements, usually RomComs. There is two I really enjoy. One is rather tropey and childish, but it is still very cute. Another one I think is rather unique.
By the way, who is Kim Dal-Young? Were you talking about Lim Dal-Young, author of Freezing, Black God, Aflame Inferno? Or is it someone else?
There are usually no unstable girls, and no depresso. Modern webtoon are usually about MC getting a second chance, being ridiculously overpowered, and stomping everyone. Is it edgy? Usually. Is it depressing? Well, depends on what you consider to be depressing.
Any case, that's only my opinion, but my general observation is anime and manga nowadays are skewing unto the edgy sadboiis, if not for cutesy idol animes, and mechas trying to spew political correctness.