As per these instructions: https://wikitech.wikimedia.org/wiki/Yubikey-SSH-FIDO#Instructions
I have generated a new SSH key for myself, backed by my Yubikey 5 NFC (Firmware version: 5.2.7)
I'll add this new key and then remove the classic key as a second step.
New public key:
sk-ecdsa-sha2-nistp256@openssh.com AAAAInNrLWVjZHNhLXNoYTItbmlzdHAyNTZAb3BlbnNzaC5jb20AAAAIbmlzdHAyNTYAAABBBHFN1sWcajd9cxr4KDxjDvBYxgyuSvz13W0uer7L1pnlrd5LTKGfsQDRoYgsNlVgMlVkXk6kMWGt+Zt4dokHhdQAAAAEc3NoOg== Yubikey-5-NFC-btullis
Note that I was unable to use an ed25519-sk, presumably because the firmware of my yubikey is too old.