So you'd register both keys. Or if you own more, you'd register at least two of them and at least one stays somewhere safe (but like, not in a bank safety deposit box, maybe the sort of place you keep a passport). This way, when inevitably your toddler throws mummy's key ring into a fast moving river, it's just very inconvenient and doesn't ruin your whole year. After you call somebody to bring a spare car key, and ask the toddler to think about what they did, go revoke all those now useless keys and order a new FIDO authenticator.

Edited to add: Even if they started identical you can reset any Yubikey, making the keys inside it random - and very paranoid people might want to before using it, since you don't know what happened to the keys inside it before you got it.

Then I'm going to sit with my wife and do that for some of her accounts and she will hold my backup.

edit for clarification, you really do need to have two devices with you to safely enough register 2fa, but obiously it is not safe to keep them both with you after initial setup, in case you lose them both. For the most part you just switch it on for everything with dual keys somehow (even if one registered key plus one Yubi Authenticator OTP).

For services that only actually enable one key, if they have emergency backup codes keep them in password manager, physical safe or a somewhere in your home depending on your threat level and the risks of the particular service being compromised.