Honestly, I think there are a fair number of indie games, especially the ones that lean toward freeform and slower play, that arose partially as a contrast to more combative styles of social play. If you play Sign in Stranger, 1001 Nights, Bliss Stage, Ribbon Drive, Microscope, Fall of Magic, Companions’ Tale, Silver & White, etc. etc. they all approach social relations fundamentally differently. But it sounds to me like you’re asking about something that has dramatic but less coercive social stuff in a fairly trad-leaning campaign-length GMful game, and that is somewhat less common, for sure, just because of the tendency to unify systems such that everything works kinda like combat. But if you move beyond that approach, a lot of things are theoretically possible. If you want a game that combines intense action with more open-ended social stuff, my go to suggestion is Bliss Stage, which I think continues to be hugely underrated.