When a coworker of mine was going through it and sounding like he was depressed, I basically called him out on it but focused on giving tips for positive self talk.

1 is instead of saying something directly self-deprecating, say something positive but however sarcastic you want to be. Instead of "Why am I so stupid" for making a mistake, you should be saying "wOw, I aM sO sMaRt". It satisfies both the need to insult yourself and for compliments and is supposed to be a way to initially break that cycle of negative talk. I imagine that whole trend of slang being used ironically until it's used legitimately works similarly.

2 is to force him to give himself a specific, genuine compliment. When he's complaining about his bowling skill, go "Hey! Friend, give yourself a compliment. Say how good you are at this other task/sport." (Ideally he'll go "hell yeah I'm amazing at that!" But I don't know you or your friend)

Like I said, this worked to help pull a friend of mine out of it, and is something I try to keep in mind for myself as well, but everyone is different.

A more general universal truth is that it's a lot harder to break a bad habit if you don't have a good habit to replace it with. Encourage good habits and it will be easier to discourage bad ones.