The problem may be caused by an interaction with “Another Windows Session Manager” and/or the “Gnome Extension Manager”. I installed both due to my desire to have something similar to hibernate and the hints I got from @wove and @wjt but I encountered problems with it.
Apparently the problems have been resolved in the same mysterious way as they started. Currently everything is working without any problems. I am still curious, what could have caused the misbehaviour. I had a deficient Gnome extension installed, which was disabled. This might have been the reason, but I am not sure.