It's only used for Yubi-OTP, which I personally don't know any services using it. Most of the MFA put in place is FIDO2-compliant, which doesn't use this privat

It's only used for Yubi-OTP, which I personally don't know any services using it. Most of the MFA put in place is FIDO2-compliant, which doesn't use this private key and cannot be traced back to a specific Yubikey serial number on the other end. Factory resetting the key will not reset the Yubi-OTP private key (which is burnt into its memory and never leave the device), but it will however invalidate any FIDO2 credentials (either resident and non-resident) from the key. The Yubi-OTP private key is also one way of certifying that the Yubikey is genuine.