>So I don't really understand how this can be said to be a hardware security token.
No one claimed it's a hardware security token, but the private keys are stored in iCloud Keychain, which is end-to-end encrypted. Apple cannot access your private keys even if iCloud is compromised by an external attacker or employee.
If you're curious about the security engineering, you should watch the "Synchronizing secrets" part of this Black Hat talk from 2016: https://youtu.be/BLGFriOKz6U?t=1353 or you should read the "Synchronization security" section of the "About the security of passkeys" support doc: https://support.apple.com/en-us/HT213305