There was a theoretical deadlock between the worker trying to emit a
signal at the same time as we were waiting for it to shutdown the
notification (while holding the lock).

The deadlock was particularly annoying because we didn't really need to
wait for the shutdown and because it wasn't possible to signals to
arrive while waiting for a start.  Attempting to deal with start and
stop in an asymmetric way could have lead to other weird situations,
however.

Drop the lock while waiting for the worker thread to start.  This means
that we face the possibility of multiple waiters on the cond at the same
time, so we need to make more of a state machine.

https://bugzilla.gnome.org/show_bug.cgi?id=742599