No, they do not provide a raw token you forward to the relying party, so it cannot be looked up later. And the data they do provide is compared against a public

No, they do not provide a raw token you forward to the relying party, so it cannot be looked up later. And the data they do provide is compared against a public key that guarantees it is non-unique to you. Look up Zero Knowledge Proofs, or Kagi's Privacy Pass, if you want to see details.