Fate is a general purpose RPG that doesn’t have any assumptions about a rest cadence. There are more specific games that use its rules (I think there’s a dresden files one that’s popular). Just the core rules work fine, but do require players to be more narratively minded and synchronized for it to really sing.
I don’t know gurps very well but I don’t think it’s built around rests at all.
I don’t think pbta games are generally built around a long rest cadence, either. They tend to have a lot of mixed success on ability use, rather than a hard limit.
The wod/cofd games aren’t centered around long rests, either. In vampire: the requiem, for example, the cool vampire powers are pretty much all at-will, require blood, or sometimes willpower. Blood is mostly narratively limited - you can get it whenever you can find someone to bite, generally. Willpower comes back over time but faster if you hit narrative beats. But generally if you have, say, Dominate, you can just do the vampire dominating gaze on people. The games typically aren’t played as dungeon crawlers though, and the limits tend to be more social or “should you?” rather than DND’s “can you?”.
One of the problems with the long rest cadence is the first fight is typically not a real threat. It’s only the last one where you’re strapped for resources that has real at hand tension. That kind of sucks, honestly. You see posts sometimes where people complain about filler fights that are just there to drain resources are kind of boring.
Making everything per-encounter is probably the easiest fix for a dnd-like game. Make some classes ramp-up, some ramp-down, and some steady.