Since support for legacy status icons is implemented by extensions
nowadays, they need to undo the call to manage_screen() when they
are disabled.
Right now that means bypassing garbage collection with an explicit
call to run_dispose() on the Shell.TrayManager. That works, but is
rather ugly.
An explicit unmanage_screen() method is a nicer option, and will be
useful to us as well to deal with X11 going away (once Xwayland
crashes don't bring down the entire session).