This feature is intended for clients that want to signal a desktop shell
their busy state, for instance because a long-running operation is
pending.
The API works in a similar way to g_application_hold and
g_application_release: applications can call g_application_mark_busy()
to increase a counter that will keep the application marked as busy
until the counter reaches zero again.

The busy state is exported read-only on the org.gtk.Application interface
for clients to use.

https://bugzilla.gnome.org/show_bug.cgi?id=672018