Are hardware keys private/trackable across services? [Hardware]

I know hardware keys such as yubikeys are extremely secure, basically perfectly secure if you don't get physically pickpocketed, but are they private?

My dissosciated google account is whining and begging me to link a phone number on one of my computers, and I'm wondering if I could link one of my yubikeys to authenticate it instead, then remove the key from the account and move on.

I've found a few vague mentions of them as private alternatives, but I …

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