The wayland issue should be gone in bookworm/sid. As stated in https://gitlab.gnome.org/GNOME/gdm/-/issues/103, https://gitlab.gnome.org/GNOME/gdm/-/merge_requests/128 is merged (in gdm 40). It supersedes https://gitlab.gnome.org/GNOME/gdm/merge_requests/37
I cannot tell about the initial gdm3 "ICELockAuthFile fail: Already exists" Xorg related issue. It seems unrelated. Cheers, Alban