I would encourage you to read around a bit more - what you're describing is actually quite a bit more crunchy than the combat systems I already use! Class-specific combat actions are still quite a D&D mindset.

Here's a few to look at:

Masks - perhaps the most popular Powered by the Apocalypse game. This is fairly similar to how you describe - you have fairly broad combat Moves ("Unleash Your Powers" etc), and the players and GM flesh out the details and the consequences.

Blades in the Dark - the original Forged in the Dark game. Here, there are no special rules around combat at all. "I bash down the door" and "I stab the other guy" are both treated the same way - the players and GM make sure they're on the same page for what the action is and what the potential consequences are, and you roll and find out what happens.

Note with both Blades in the Dark and Masks, NPCs don't roll at all, even in combat. "You get stabbed while attempting to stab the other guy" is instead a consequence of a failed roll or partial success (in which case you probably both hurt each other).

Dune - Adventures in the Imperium - this is an interesting one, which does have a mildly crunchy Conflict system. However, any type of conflict is done with the same system - whether it's House politics or a knife fight or a spy sneaking through a palace. One thing here is that minor NPCs can be defeated by a single action - although any appropriate and successful action can do this, it doesn't single out combat actions. You could stab a Harkonnen with a knife or intimidate him into running away, and both use the same mechanic - just a skill check - although the difficulty may differ between the actions, depending on the situation and your assets.

There's also a number of "middle ground" games where you do have an action economy (e.g. "one minor and one major action per turn") but are kind of loose in what is meant by these actions. This would include Stars Without Number, Traveller, and many Old School Renaissance games. Here you might have something like turns and hit points, but you don't select from a list of official moves - you decide an action that makes sense, and the GM makes a ruling on how to do it (although the books often have a lot of suggestions and advice and examples), which typically is some sort of skill roll or skill roll modifiers.