panel: Rewrite the app menu to use the new "sync" pattern

panel: Rewrite the app menu to use the new "sync" pattern

The existing app menu was a kludge of legacy code that tried to manage
a bunch of state, and had a number of issues:

 * It didn't properly manage visibility when combined with multiple
   apps and the overview.

 * It didn't properly manage reactivity when tabbing away from a busy
   app to another app.

 * It didn't properly disconnect signals when going from one app
   to nothing.

and countless others. Rewrite it to use the new "sync" code pattern,
where we centralize all state management and do transitions from that,
rather than strange and quirky control flow.

https://bugzilla.gnome.org/show_bug.cgi?id=705898