External mouse/keyboard @ LG display no longer recognized over thunderbolt
IT crowd to the rescue...

It was not the macbook (tried everything: updating MacOS, resetting SMC, NVRAM, updating drivers, safe mode etc.). Simply disconnecting and reconnecting the display from the power solved the problem.

My only excuse is that the monitor was in standby many times during these trials, so I kind of thought it was turning off and on again. That wasn't enough, though.