classic: Add X-GNOME-SessionRegisters

GDM has supported sessions registering with it for a few years now so
it can know when to shut down the greeter. Having the GNOME Classic
session declare that it will register itself allows GDM to avoid
executing a fallback codepath.

This has been supported with the regular GNOME session for a while,
and this session was likely forgotten about when it was added there.

(cherry picked from commit a79d2afb)

Part-of: <https://gitlab.gnome.org/GNOME/gnome-shell-extensions/-/merge_requests/202>