I strongly and whole heartedly recommend "a monster calls" by Patrick Ness (please read the book instead of watching the movie, it's not even that long, I remember it was kind of a short read), It's labeled as a young adult, but I kid you not I had tears in my eyes when I read it and I'm well in my twenties. The MC is a boy, and while it's not explicitely said, there are clear signs that he struggles with depression, bullying, and profound sadness.
Also, there's an M/M novel called "Broken" by Nicola Harken in which one of the main characters had severe depression and struggles with suicidal thoughts (For the record, I didn't like it much because the writing style wasn't much my cup of tea, so I gave it a 3/5 stars, but some people gave it 5/5 so maybe give it a try?)
Anyway, I'm also always looking for books that talk (seriously and in a well researched way) about mental illness and psychological struggles so if you find something that really appeals to you, do share it ^^
Can someone recommend me a book (not a manga, but a "real" book), where the main character has social anxiety and/or depression (but preferable with social anxiety), that is a good read? It can have a bad ending, but I would prefer a happy one ^^