Is it on a tty in embedded mode? If so does switching ttys using CTRL+ALT+F{1…10} work? Usually the display manager is on F1 or F7. If it’s not in embedded mode, does Left Alt + Enter work?
EDIT: Re-read and realized I didn’t understand completely. You’re starting it with your display manager. I’m not sure how you would kill it in that case.
Does Bazzite use a gamescope session on wayland by default? Gamescope has a bug which prevents the wayland client from drawing the steam overlay. I suppose it’s unlikely to be the same issue but I happen to be dealing with it on my system (not Bazzite) so I immediately made the connection.