This is how we have been working around #303 in Endless OS for the case where PulseAudio is brought up in the user session before PulseAudio in the GDM session has finished, in which case the later PulseAudio instance fails to register Bluetooth profiles with bluetoothd.
This depends on https://lore.kernel.org/linux-bluetooth/20210611020728.15233-1-jprvita@endlessos.org/ on the BlueZ side.