I had this issue also, it's just resolved itself.
I am on Monterey 12.3.1 (newest at time of writing)
What I did was unplug the display from power, let it sit for a few minutes, plug it back into power, then put the thunderbolt 4 cable into the display and then into the laptop.
But this only worked after letting it sit like that, plugged in, for like 5-10 minutes.
Also one time literally just switching which end was plugged into the display fixed it...
I don't know if it is required to do this every time you switch macs, which I planned on doing a lot of (thunderbolt is supposed to be the ultimate universal port, right?) but it is unacceptable for this to occur every time I switch macs. (As it has, every time I've tried to hot swap them.)
Especially costing what it does.