I guess that this issues is also related to
where gdm does not read the local configuration files.
journalctl -b|grep gdm shows a lot of entries like
gsettings[2343]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gnome-session-b[2342]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gnome-shell[2368]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
at-spi-bus-laun[2471]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-sharing[2558]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-sound[2579]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-housekeepin[2582]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-smartcard[2570]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-usb-protect[2562]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-color[2566]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-a11y-settin[2580]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-keyboard[2567]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-wacom[2571]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-power[2583]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-datetime[2576]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-media-keys[2577]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gjs[2765]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
gsd-xsettings[2581]: Unable to open /root/.local/share/flatpak/exports/share/dconf/profile/gdm:
Adaptation in /etc/profile.d/flatpak.sh does not really help here.