Moves happen when everyone at the table agrees that they happen.
Rarely, this is purely logical and consequential - someone takes harm, so the Keeper makes a harm move.
Often, this is pretty danged obvious - someone wading into a combat situation is probably looking to kick some ass, someone working a ritual is looking to use magic, or maybe use big magic.
But there have already been times when you weren't sure if someone was trying to trigger a move or not, right? Are they trying to manipulate an NPC or just making small talk? Are they trying to investigate a mystery or just asking you for a better scene description? So you ask them what they're trying to do and break one way or the other depending on the answer.
And of course there are times when someone just says they want to make a move, with little or no extra description. What do you say then? Well, I know what you should be saying then.
"Cool! What's that look like?"
So, leveling up is a move too. It's not a mechanical artifice separate from the story. Sometimes it's pretty danged obvious how it happens, especially if you're not grabbing a move outside your playbook. Hunches make perfect sense for The Spooky, their playbook of origin, because an uncanny six-year-old abruptly showing up in front of you and telling you to run is really just par for the course for uncanny six-year-olds, right?
But when other playbooks grab it, the lines get a little blurrier. The Divine, The Chosen, The Monstrous - all of them are on a level where uncanny appearance is probably well up there. The Expert, The Initiate, or The Spellslinger may have finally decided to dedicate some space to a proper divination orrery - The Flake and The Wronged did the same, except to plot out the true depths of the conspiracy they're about to blow wide open.
...and then there's The Mundane.
And maybe that schtick doesn't really fit the other playbooks as your players have realized them, either. That's fine. This is a world where any of the PCs can Use Magic. Maybe it's not a good idea for a few of them, but it's a world where the supernatural exists and you can, say, make the inexplicable acquaintance of a magical corgi who fetches you next week's alternative weekly newspaper this week. Or maybe you're not trying to stumble on people in trouble just in time to save them, you're trying to do what you've always done, which is get away from all this madness, but something out there obviously has other plans!
So when you ask your player "Cool! What's that look like?" to find out the answers to all your questions, it's not to find traps in their narrative, places where they're weak and you can exploit them. You're the Keeper. You can drown the world in demons if you want and no one can stop you. You're looking for their narrative so you can play along, so when somebody honks an investigation move you can narrate to your player with Hunches just what's bunching their hunch before you zoom the camera halfway across town, narrate a bit, and call for a Sharp roll.