Now same issue with LTS kernel, so my issue most likely not related to the kernel.
In the journalctl I can see several errors about display :0 not available, e.g.
Jan 10 17:27:55 cubitus gnome-screensav[921]: gnome-screensaver: Fatal IO error 11 (Die Ressource ist zur Zeit nicht verfügbar) on X server :0.
Next many apps exit with error code 1, e.g.
Jan 10 17:27:55 cubitus gnome-session[878]: gnome-session-binary[878]: WARNING: App 'org.gnome.SettingsDaemon.XSettings.desktop' exited with code 1
and then the session is stopped and daemons killed:
Jan 10 17:27:55 cubitus systemd[1]: Stopping Session 1 of user matthias.
Jan 10 17:27:55 cubitus kernel: rfkill: input handler enabled
Jan 10 17:27:55 cubitus gnome-session[878]: gnome-session-binary[878]: WARNING: Application 'org.gnome.SettingsDaemon.Sharing.desktop' killed by signal 1
Jan 10 17:27:55 cubitus gnome-session[878]: gnome-session-binary[878]: WARNING: Application 'org.gnome.SettingsDaemon.Datetime.desktop' killed by signal 1
...
Still not clear what is causing this problem.