I don't currently know the specifics of the standards, but often key migration means signing and publicly announcing a new device's hardware public key and optionally revoking an older device's hardware public key. The private keys themselves might never leave the hardware secure enclaves (and/or other key escrow services) to do the dance of updating a keychain of public key signatures. The big "advances" in the standards over the last few years have been about moving away from the "classic" PGP/CA style PKI assumption that a user is represented by a single strong key and a hierarchy of owned subkeys and more that a user is represented by a keychain of N keys many more roughly "peers" than hierarchical and in something of a web of trust with each other where N is at least the number of devices the user owns and regularly uses, and often much more than that with various key escrow strategies. I believe the "PassKey" approach uses an escrowed sub-key per-website in many cases so the keychain gets conceptually huge. (Escrowed here is that it is a derived key using data available to some quorum of physical device keys. You can rederive escrowed keys, but you can't export physical device keys that made the escrow data in the first place. You should be able to add new device keys that can share in a quorum to get at that data, but it's a migration dance.)
To my knowledge Keybase's breakdowns of how their keychain worked, including subkey escrow and key exchanges are still some of the easiest to read on the subject of how the math works, though I don't think Keybase's "standards" entirely resemble some of the details of the final standards from FIDO, but again I also don't know enough of the specifics of FIDO's standards as I'd like.