Bitwarden has a passkey service + a paid totp service, so I can always use either to log into whatever within two clicks. Yeah it's less secure than a physical keychain but... Whatever, it's better than passwords and as easy to use.
In any case, if you atore the backup codes in a place where you can lose them, that's on you. Upload them into somewhere you control that has good privacy laws.
... How about going for a EC key?? Staying with RSA is stupid at this point.