I use Aegis, which automatically backs up with each change to the database to a folder that gets synced to a couple of different computers via syncthing.
For backup codes, I have a separate keypass database that’s backed up to a couple of places. I thought about using Bitwarden for this backup, but having my 2FA backups in the same place as my passwords kinda defeated the point, IMO.
Anyway, this system has worked well for me.
This is the first time I’m hearing about this feature and am interested. But I feel like it would be better to use a different password than your master for these higher security logins. The thought being that, if someone has access to your passwords, they likely have access to your master password as well, unless they had access to an already unlocked vault.