I'm not perfectly fluent in the U2F/WA protocol but shouldn't it be possible to have two devices but one is programmed to only accept registration and not allow normal operation?
That way you could put the fully functional one into a bank deposit and use the other to register that key...
It seems like you could use existing tooling to generate the phrase and then use some existing code/processes to derive the key backing the token's u2f private key?
The problem that we need to solve securely, is that you as a user must be sure you know all devices with that private key, i.e. no one else can trigger a backup without you knowing that, even with a temporary access to the key.
Isn't what you're discussing (prevent unknown backups) more a function of how the private key is held in the Solo itself (and in my example, how securely your seed phrase is stored)? Or is there an element of U2F that I'm missing here? (Does the token itself have an identity that you want to be unique while still preserving the same key for authentication, or is there some other detail I'm missing?)
You can, for example, set up a pin or passphrase, however the fido2 protocol doesn't (necessarily) work like that. You buy a key, and you just start using it. There are multiple options to implement a backup protocol, but no standard one to the best of my knowledge. My original point was just that in designing such a protocol, it's important to consider this "unknown backup attack".