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 eeabdd15 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.
Fixes #5714 (closed) Fixes #5722 (closed)