The numeric id is fine as well:
$ id
uid=1000 ...
Some more news here: checking the gdm service I found the following error:
Mai 01 00:29:40 schwarzschild systemd[1]: Started GNOME Display Manager.
Mai 01 00:29:43 schwarzschild gdm-launch-environment][1660]: accountsservice: Could not get current seat: No data available
Mai 01 00:29:48 schwarzschild gdm-password][2030]: accountsservice: Could not get current seat: No data available
Mai 01 00:29:50 schwarzschild gdm-password][2030]: gkr-pam: unable to locate daemon control file
I’ll dig deeper into this and keep this thread posted.
But thanks for the help so far!