OK, so after reflash I’ve restored the gziped content of /var/lib/bluetooth and all my previously paired devices appeared as paired and are working OK.
So this is a very easy way to backup Bluetooth pairings.
This only works within the same device I think, because the adapter’s own MAC address is part of the folder structure… Moving the “history” to another device doesn’t make sense though, because the client devices won’t recognize the new device anyway.
Yes, it is a backup that will work only if restored to the same device. But it’s still very useful, e.g. in case of my car kits which make problems when pairing. As long as I don’t delete the pairing from the car kit side, I can always restore this backup to my phone (e.g. after reflash) and instantly have a working pairing.