qtui: Refactor the system tray implementations

qtui: Refactor the system tray implementations

Replace the mess of virtual methods and init() and other weird
shenanigans by a cleaner architecture. Handle mode/state changes
in the base class and let the implementations explicitly act on
changes. This should make it much clearer how the implementations
behave if mode or state change.

Simplify the D-Bus parts of StatusNotifierItem quite a bit by
keeping the SNI watcher always alive; no need to kill it when
unregistering. Add error handling to the final D-Bus registration
call and fall back to the legacy icon if something went wrong.