This reverts the revert commits d264dbf1
and e97dc693.

Even though the GNOME Shell extension's logic to avoid double-starting Florence
is flawed, it is only flawed when one 0. uses Florence; 1. uses a system where
Florence needs more than 1 second to start; and 2. one waits more than 1 second,
but less than the time it takes to start before clicking on the icon again.

The alternate option this commit reverts has worse problems: Florence sometimes
is not hidden on startup, which affects all users, and requires an ugly
workaround in the test suite (which is broken on feature/stretch currently, so
this comes with a maintenance cost). Besides, it eats memory for everybody,
while I expect the vast majority of users don't actually use Florence.

So, all in all, I prefer going back to the behaviour previously implemented
in feature/stretch, that I had reverted earlier today.