Reframing:
The thing he wants is to keep Haru. He keeps saying that he wants to be the man of Haru's dreams, but then he's just whining and feeling sorry for himself. Haru has given him a list. Haru has told him exactly what he needs to feel safe. Jaeha shouldn't be approaching those as a checklist of things to do before Haru will finally get over Jaeha's past so that Jaeha can have a chance; this is what being Haru's dream is. If he conceptualises himself as being the man of Haru's dreams, having woken up from this extremely long period of inebriation, watching the way he set his own life on fire, then figuring all of this out is part of being that man. Getting therapy, talking to the people Park Yoo-min suggests him, cutting his father off, these are all steps to becoming that person. Maybe not sufficient, but definitely necessary. It's not that doing them will get Haru to finally recognise him and tell him he's done good; he needs to want them. He needs to want to be that person. The way he'll get Haru to love him, the way he'll get his chance to feel stable, to have Haru want to "become monogamous again" and be with him, is being trustworthy about being that person.
Many of those steps feel scary. So maybe what he should do is write them down, all of them, and then think about them and write down why they feel scary. What feels scary about them. What failing would look like, and what succeeding would look like. What he should do if he fails, what he expects to fail. And then come up with plans for those. Figure out what he should feel about them, and what he actually does feel about them, and why, and why he's feeling that and not what he should, whether those are compatible, whether he's attached to feeling one way or another and why, how much he can flex that, what he's willing to sacrifice. Which parts of his brain are important, and which are not.
He spends... quite a while writing all of this down, and staring at it, and erasing and rewriting it. Not so long that he's still doing it by the time Haru's back, but mostly because eventually he gets cross-eyed and headachey from all of the staring at his own brain he's been doing and has to take a break to go work out in the personal gym he has in his absurd house so that he can forget he has a brain in the first place. He's still there when Haru's done with his dungeon.