GUI does not start, but GPU driver seems fine

I installed Ubuntu 22.04 on a fresh computer and I can't get the GUI mode to work.

• It seems that the graphics card works fine. I even confirmed that CUDA works by doing a bunch of matrix multiplications on the GPU:

nvidia-smi
Wed Oct 19 08:23:13 2022       
+---------------------------------------------+
| NVIDIA-SMI 515.76       Driver Version: 515.76       CUDA Version: 11.7     |
|-------------------------------+----------------------+----------------------+
| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |
| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |
|                               |                      |               MIG M. |
|===============================+======================+======================|
|   0  NVIDIA GeForce ...  Off  | 00000000:01:00.0 Off |                  N/A |
|  0%   29C    P8    14W / 170W |   3176MiB / 12288MiB |      0%      Default |
|                               |                      |                  N/A |
+-------------------------------+----------------------+----------------------+
                                                                               
+---------------------------------------------+
| Processes:                                                                  |
|  GPU   GI   CI        PID   Type   Process name                  GPU Memory |
|        ID   ID                                                   Usage      |
|=============================================================================|
|    0   N/A  N/A      2169      C   ...lia-1.8.2+0.x64/bin/julia     3173MiB |
+---------------------------------------------+

• I tried gdm3, lightdm and sddm. All three fail:

systemctl status display-manager.service
● gdm.service - GNOME Display Manager
     Loaded: loaded (/lib/systemd/system/gdm.service; static)
     Active: active (running) since Wed 2022-10-19 08:16:37 CEST; 3min 4s ago
    Process: 1303 ExecStartPre=/usr/share/gdm/generate-config (code=exited, status=0/SUCCESS)
   Main PID: 1316 (gdm3)
      Tasks: 3 (limit: 76064)
     Memory: 5.2M
        CPU: 2.179s
     CGroup: /system.slice/gdm.service
             └─1316 /usr/sbin/gdm3

Okt 19 08:16:51 janpc gdm3[1316]: Gdm: GdmDisplay: Session never registered, failing
Okt 19 08:16:51 janpc gdm3[1316]: Gdm: Child process -1951 was already dead.
Okt 19 08:16:51 janpc gdm-launch-environment][1993]: pam_unix(gdm-launch-environment:session): session opened for user gdm(uid=127) by (uid=0)
Okt 19 08:16:51 janpc gdm-launch-environment][1993]: pam_unix(gdm-launch-environment:session): session closed for user gdm
Okt 19 08:16:51 janpc gdm3[1316]: Gdm: GdmDisplay: Session never registered, failing
Okt 19 08:16:51 janpc gdm-launch-environment][1993]: GLib-GObject: g_object_unref: assertion 'G_IS_OBJECT (object)' failed
Okt 19 08:16:51 janpc gdm3[1316]: Gdm: GdmLocalDisplayFactory: maximum number of X display failures reached: check X server log for errors
Okt 19 08:16:51 janpc gdm3[1316]: Gdm: Child process -2036 was already dead.
Okt 19 08:16:51 janpc gdm3[1316]: Gdm: GdmDisplay: Session never registered, failing
Okt 19 08:16:51 janpc gdm3[1316]: Gdm: Child process -2036 was already dead.

× lightdm.service - Light Display Manager
     Loaded: loaded (/lib/systemd/system/lightdm.service; indirect; vendor preset: enabled)
     Active: failed (Result: exit-code) since Wed 2022-10-19 08:21:22 CEST; 22s ago
       Docs: man:lightdm(1)
    Process: 1550 ExecStartPre=/bin/sh -c [ "$(basename $(cat /etc/X11/default-display-manager 2>/dev/null))" = "lightdm" ] (code=exited, status=0/SUCCESS)
    Process: 1553 ExecStart=/usr/sbin/lightdm (code=exited, status=1/FAILURE)
   Main PID: 1553 (code=exited, status=1/FAILURE)
        CPU: 205ms

Okt 19 08:21:22 janpc systemd[1]: lightdm.service: Scheduled restart job, restart counter is at 5.
Okt 19 08:21:22 janpc systemd[1]: Stopped Light Display Manager.
Okt 19 08:21:22 janpc systemd[1]: lightdm.service: Start request repeated too quickly.
Okt 19 08:21:22 janpc systemd[1]: lightdm.service: Failed with result 'exit-code'.
Okt 19 08:21:22 janpc systemd[1]: Failed to start Light Display Manager.

systemctl status display-manager.service 
● sddm.service - Simple Desktop Display Manager
     Loaded: loaded (/lib/systemd/system/sddm.service; enabled; vendor preset: enabled)
     Active: active (running) since Wed 2022-10-19 08:00:28 CEST; 13min ago
       Docs: man:sddm(1)
             man:sddm.conf(5)
    Process: 1236 ExecStartPre=/bin/sh -c [ "$(cat /etc/X11/default-display-manager 2>/dev/null)" = "/usr/bin/sddm" ] (code=exited, status=0/SUCCESS)
   Main PID: 1241 (sddm)
      Tasks: 2 (limit: 76064)
     Memory: 18.8M
        CPU: 127ms
     CGroup: /system.slice/sddm.service
             └─1241 /usr/bin/sddm

Okt 19 08:00:28 janpc sddm[1241]: Initializing...
Okt 19 08:00:28 janpc sddm[1241]: Starting...
Okt 19 08:00:28 janpc sddm[1241]: Logind interface found
Okt 19 08:00:28 janpc sddm[1241]: Adding new display on vt 1 ...
Okt 19 08:00:28 janpc sddm[1241]: Loading theme configuration from ""
Okt 19 08:00:28 janpc sddm[1241]: Display server starting...
Okt 19 08:00:28 janpc sddm[1241]: Adding cookie to "/var/run/sddm/{3e773afd-3a04-444e-8e05-140658ba459a}"
Okt 19 08:00:28 janpc sddm[1241]: Running: /usr/bin/X -nolisten tcp -auth /var/run/sddm/{3e773afd-3a04-444e-8e05-140658ba459a} -background none -noreset -displayfd 17 -seat seat0 vt1
Okt 19 08:00:28 janpc sddm[1241]: Failed to read display number from pipe
Okt 19 08:00:28 janpc sddm[1241]: Could not start Display server on vt 1

• Any ideas?