Dear Maintainer,

On a fresh 12.10 install I modified the user default shell from bash to zsh.
Unexpectedly after this change, applications located in /usr/games/ where not
shown anymore in gnome-shell.

Step to reproduce:
- Install Debian Bookworm 12.10
# apt-get install flightgear pingus [and some other games...]
- Login to gnome-shell
- Show applications tiles [games are present]
# apt-get install zsh
# vipw
- Change user shell from /bin/bash to /bin/zsh
- Restart computer
- Show applications tiles [games are missing]

Investigation shows that $PATH is missing /usr/local/games and /usr/games
(start gnome-terminal and "$ echo $PATH").
I found some old threads linking this issue with how wayland initialize the
environment variables:
https://bugzilla.gnome.org/show_bug.cgi?id=736660
https://unix.stackexchange.com/questions/317282/set-environment-variables-for-
gnome-on-wayland-and-bash-on-virtual-terminals-or
https://superuser.com/questions/1149622/gnome-3-22-how-to-change-the-path-for-
the-shell
https://github.com/systemd/systemd/issues/7641

It is not clear to me how today $PATH is initialized by wayland. There is one
Wiki page for Debian https://wiki.debian.org/EnvironmentVariables which is
rather generic. It would be helpful to explicit the interaction between gnome-
shell, wayland, pamd, systemd and shell.