For avant-garde there are some stylistic elements you can pick up on such as a sense of things falling apart or even distress based on the way something is being played. The other musicians may add their own ‘voice’ in on the story good or bad.
It can still be a compelling story being conveyed but it’s not necessarily something you’d put on when you’re intending to relax.
If they’re able to “pick up on other’s styles while playing” then they understand music theory enough to do that.
That falls under “improvisation while understanding musical theory.”
My criticism of avant-garde was different, not directed as a blanket statement about all jazz improvisation.
For avant-garde there are some stylistic elements you can pick up on such as a sense of things falling apart or even distress based on the way something is being played. The other musicians may add their own ‘voice’ in on the story good or bad.
It can still be a compelling story being conveyed but it’s not necessarily something you’d put on when you’re intending to relax.