The issue has been going on for a while (smelly air, moisture blowing
into the cabin, etc...) for a few days. This morning, the AC started
to make a clicking sound that went away when I turned it off. I turned
it back on and heard a belt squeal for a few seconds, then the car
stalled.

Now, the car runs fine as long as I don't turn on the AC. Stalls as
soon as the AC kicks in if I turn it on.