Dear Maintainer,

On a new install running bookworm my regular user has the wrong PATH
set. The path used matches ENV_SUPATH from /etc/login.defs.

I think this is because sway inherits the environment from the desktop
manager (gdm3) which is run as root.

One solution I found in #968910 (message #15) is to modify
/usr/share/wayland-sessions/sway.desktop to run sway in a login shell.

Another similar bug is #1011088 (zsh) but I installed Gnome and logged
into a Wayland session and my user got the correct PATH in my bash
shell (did not test under zsh, but I don't expect a difference).