FIDO involves creating a new public/private key pair for each website, to prevent cross website tracking. The keys are derived from a secret stored on the device, so the device doesn't need to store anything but that secret, which enables it to be used with a limitless number of websites.

Edit: there seems to have been a paper that studied the very question of "can you create keys asynchronously so that you can later use them with a backup key": https://eprint.iacr.org/2020/1004.pdf https://www.youtube.com/watch?v=urJ2DhpLAEk

I need to read the paper however on how feasible an implementation of this is, and how much buy-in it needs from website and browser vendors.