Hi
Please apply the commit 24b065727ceb ("Bluetooth: Return NOTIFY_DONE for hci_suspend_notifier") to the v5.8.y branch as well. As the commit message says it fixes actually an issue:
The original return is NOTIFY_STOP, but notifier_call_chain would stop the future call for register_pm_notifier even registered on other Kernel modules with the same priority which value is zero.
The commit misses a Fixes tag on 9952d90ea288 ("Bluetooth: Handle PM_SUSPEND_PREPARE and PM_POST_SUSPEND") and so was not backported as well.
This was affecting Felix Dörre (https://bugs.debian.org/964839#65) with an out of tree module, but as the commit explains the issue seem to be more general.
Thank you already,
Regards, Salvatore