So I’m going to ask you directly does AW provide rules or rulebook guidance for how to handle situations where the player has the PC do an action that isn’t a move?
Explicitly, like, "here's what to do when the action isn't covered by a player move"? It doesn't.
Doesn't need to either.
There is a general rule: when the player looks at GM
* to see what happens next, GM makes a GM move. Player moves are
exceptions to this general rule, when the action PC takes is covered by a player move available to them, GM doesn't just make their move, instead both GM and player work through the wording of the move and do what it says.
*If the GM can't physically know whether player is looking at them or not, say, because it's online play or GM or player is blind, just use your brain. Treat it as "there is a questioning pause" or whatever. If player doesn't make a pause and doesn't care what results their action will have, then, who cares?
In Dungeon World, Fighter has a move "Bend bars, lift gates". It says:
When you
use pure strength to destroy an inanimate obstacle, roll+Str. On a 10+, choose 3. On a 7-9 choose 2.
- It doesn’t take a very long time
- Nothing of value is damaged
- It doesn’t make an inordinate amount of noise
- You can fix the thing again without a lot of effort
So when Fighter tries to break down a door with a kick, this move is triggered. They roll +Str, get, let's say, 9 and choose, let's say, "Nothing of value is damaged" and "It doesn't take a very long time". GM then narrates what results this will have, knowing that her narration can't involve something of value being damaged or the process taking long time, but can involve, say, goblins in the dungeon hearing the ruckus.
When Cleric who doesn't have access to this move tries to break down a door with a kick, nothing of this happens. GM just makes a move. Any move she likes. Including, say, "This is of no use. The door doesn't budge, and you hear goblins running in through another passage. What ya gonna do?"
For the record: I'm using Dungeon World because it's the only game where I can think of a mundane action being covered by a move for one playbook and not for another, and, for the record, I don't think it's a particularly good design.