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I think if Dazai got a psych diagnosis it would be Borderline Personality Disorder. Hear me out. He hits just about every sympton listed on the Mayo Clinic's website. Suicidal and feelings of emptiness are shown throught BSD. We see him being involved in risky behavior (gambling, drinking, literally putting himself in dangerous situations/harms way). Inappropriate, strong anger is a bit harder to catch since his isn't physical or loud like Chuuya, instead Dazai tends to get sarcastic and bitter as we see in 15 or he gets "even," if someone one ups him he attempts to destroy them as we see with Fyodor and as shown with the quote Oda had about Dazai’s enemies. His relationships are rather unstable (don't think anyone will argue with me there) and there is an argument that he has abandonment issues which is why he keeps people at arms length, kinda a "you didn't leave me, I pushed you away" deal. If you're paying attention you can also catch when he's manic and when he's masking. Most of the time, he's masking. One exception is at Lupin Bar with Oda and Ango. He's not as over the top like when he's masking, but he's also much more excitable than usual. It's a subtle difference and I've found that it's not shown in the anime as much as it is the novels.
Please note: I say this as someone who is diagnosed neurospicy, so my personal experience may be at play in my analysis.