Quick Note to myself the community:
I recently replaced PulseAudio with PipeWire. Or, to be precise, I had to replace it because Gnome now has some depdencies on it.
Unfortunately, my BlueTooth headset did not work, any longer. It connected but did not show in Gnome's sound settings. I had some kernel updates pending, so my expectation was it would be resolved after a restart.
TLDR; I did the following:
systemctl --user restart pipewire sudo systemctl restart bluetooth
That worked. Maybe I'll have to do the same thing on next reboot ... I hope not ;-)