Just to close this discussion, I've finally found the answer and it has nothing to do with hardware update, sorry for the red herring ![Sad :-(]()
The real problem is that I had installed DEB package from https://www.nomachine.com/ for testing and even though I have quickly uninstalled it because it doesn't work at all under Wayland, I didn't realize just how broken their package was: one of the (many wrong) things it does is to insert a reference to /usr/NX/scripts/env/nxpreload.sh into /usr/lib/systemd/user/org.gnome.Shell@wayland.service and uninstalled NX package does not remove this from there, explaining why this service couldn't be started any more. Just removing it from there allows gdm to launch Wayland session normally.
Sorry for wasting everyone's time, retrospectively it's clear that the original question was completely impossible to answer.

The real problem is that I had installed DEB package from https://www.nomachine.com/ for testing and even though I have quickly uninstalled it because it doesn't work at all under Wayland, I didn't realize just how broken their package was: one of the (many wrong) things it does is to insert a reference to /usr/NX/scripts/env/nxpreload.sh into /usr/lib/systemd/user/org.gnome.Shell@wayland.service and uninstalled NX package does not remove this from there, explaining why this service couldn't be started any more. Just removing it from there allows gdm to launch Wayland session normally.
Sorry for wasting everyone's time, retrospectively it's clear that the original question was completely impossible to answer.
Statistics: Posted by _VZ — 2024-04-12 11:59