It is generally not possible to differentiate between systems
without bluetooth support, and systems where a bluetooth adapter
is powered down.
We work around that by tracking whether there are any set up devices,
and keep the bluetooth visible in that case, even when no adapter
is present.
However commit eeabdd150c7 moved updating the setting into the code
that handles adapter changes, which is exactly the place where we
carefully avoid changing the setting because it would be too
unreliable (devices may have already disappeared, or not yet
appeared).
Fix this by changing _setHadSetupDevices() to _syncHadSetupDevices()
and call that everywhere _sync() used to be called, *except* on
adapter changes.
https://gitlab.gnome.org/GNOME/gnome-shell/-/issues/5714
Part-of: <https://gitlab.gnome.org/GNOME/gnome-shell/-/merge_requests/2409>
4fd4b09919