

You’re going to have to look at how that process works on Ubuntu and how it differes from Xorg session start.
gdm probably looks inside /usr/share/wayland-sessions and finds sway.desktop and uses it to launch Sway.
FWIW, these are all text files. Look at them.
Sorry, I have to go now. More tonight, if you want.
Sorry what? As what user are you executing (all these) commands? Unless Ubuntu does things significantly differently than Arch and Debian, there’s something very fishy going on here. The “normal” user should not be in the root group, and root should not be in the normal user’s group.
Have you done other things beside the “fix” you mentioned?
That “fix” from your op, btw, looks totally valid to me.