After reading about a couple of KBs in this thread I decided to yolo it and install them, not knowing what to expect.
I now have the strange behaviour that I only get the error message on shutdown when running at least one specific programme, which I can reproduce on demand.
No xbox controller or other bluetooth device involved. It reinforces my suspicions that it has something to do with a dll or some other software related dependency when running certain apps.
Microsoft is really being lame about this, I have to say. But I'm not surprised.