I think an underrated part of how Katsuki seeks out Deku when he’s having a breakdown is that he expressly doesn’t want Dekus help.

He doesn’t want Deku to comfort him, try to fix anything, or make it better.
He has no motive to seek Deku out, maybe even an anti-motive, because Dekus someone who compulsively tries to help others.

Still Katsuki goes to Deku with only one goal, to be seen, to be seen by Deku

He wants this, even though for a large part of the series he’s under the impression that Deku looks down on him, with that in mind he still can’t stop his need to bare his soul to Deku when he’s at his breaking point

He confronts him “knowing” he’d be giving Deku more “ammo”, and with very loud intentions of not wanting pity, sympathy, or /anything/ from Deku

Katsuki doesn’t have a lot of(literally any) emotional intelligence which leaves him not thinking about his reasonings for things he does until much later on, he just follows his gut and doesn’t question it. Despite everything his instincts are always to trust Deku

So he goes to the person he trusts most to say “I’m hurting, and I need to feel seen, even just for a moment, just until this weakness passes. Pease just see me, acknowledge that I’m someone still, that I’m not as alone as a I feel, validate my hurt without trying to change it”