It took me a while to wrap my mind around what was going on with PATH, gdm, wayland sessions, X sessions, and systemd environment generators.
I'll try to summarize my findings here. I initially found this change[0] to be the cause, but I am still not exactly sure why or how it works. I have been informed that we may be better off using systemd environment generators[1][2] and import PATH from systemd which pulls from Debian's /etc/profile. Another suggestion is that we stop using /usr/games[3]. 0: https://gitlab.gnome.org/GNOME/gdm/-/merge_requests/92/diffs?commit_id=ccecd9c975d04da80db4cd547b67a1a94fa83292 1: https://gitlab.gnome.org/GNOME/gdm/-/issues/846 2: https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=1037084#10 3: https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=1028543#15