in terms of what made me become completely obsessed like clint/bruce, it was probably MAVG. Clint had been my favorite marvel character for years, but he actually didn't show up in the game until about 6 months after it was released, so he just was like. not there for awhile lol. and Bruce's subplot in the main campaign is so good like I cannot emphasize enough how well they write him in this game it's actually kind of crazy. so ig because there was no Clint for me to focus on Bruce filled that role and when Clint did finally show up in the game, it meant I was paying an insane amount of attention to everything they both did, and it turns out the writers were also paying an insane amount of attention to what their relationship looked like because they have *so many* interactions with each other. looking back, I can't really pinpoint when/what specifically in the game triggered the thought of "hey they'd be good together." My best guess is a combination of some of their dialogues. There's one where they mention their super-secret coffee place (in-game Clint was very concerned about Monica knowing about it, Bruce assures him he never told her), one where Bruce is offering Clint an air mattress that he can use in Bruce's room (long game related story, I can elaborate if you're interested), and some others. There were just a lot of seeds and hints that they'd had a pretty close relationship, and it made a lot of sense to me; they fit together very well. Clint is the only Avenger without super powers (this is a universe where Nat has a super-soldier serum variant, or it's at least implied she does) and Bruce's only "power" is the Hulk, something he has very complicated feelings about, but I don't think he sees "Bruce Banner" as an Avenger; he's just a vessel for the Hulk, so in this way I think they both kind of see themselves as outsiders to the Avengers and I think because of that they can be drawn to each other in a kind of weird way, cause they both don't see the other as an outsider. I think there's a subconscious recognition of "hey, you and I kinda share the same insecurity, let's become homoerotic best buds about it."
Personality-wise, I think they do a good balancing act with each other. Clint is definitely louder than Bruce but he's also good at drawing Bruce out of his shell in a natural way. Like, he's genuinely interested in what most people have to say, including Bruce, and I feel like Bruce probably isn't used to that. And I also think Bruce caught on pretty quickly that Clint is way smarter than he portrays himself to be, and for some reason this results in Clint lowering that mask a lot more around Bruce than he does around other people who also see through it (i.e., Nat and Steve).
hmm this got very long, sorry about that 😂 I'd love to hear your thoughts about them as well, it's been a minute since I've watched EMH but ik they have a similar kind-of-unexpected bond going on in that as well