Completes the SeatNew/SeatRemoved pair from the prior commit. The
emit_seat_removed public method was added but not wired to any shutdown
path; this commit hooks it into wait_for_shutdown's return path so
subscribers (e.g. SDDM's LogindSeatManager) observe seat departure
before the D-Bus connection drops. SEAT_PATH is reused from main.rs's
existing constant rather than introducing a new placeholder string.
vasilito
e6e4289113