> Citation needed? Yubico authenticator doesn't (the secure enclave is the Yubikey). I'd be very surprised if MS Authenticator and Authy (which I don't use but are the most popular apps that I know of) support such backups

Google Authenticator has an export option that I've used in the past, so that one does it for sure. Authy allows cloud-based synchronization in any case, so exporting seems quite possible. MS Authenticator also allow cloud sync, so probably exporting is not difficult.