Sorry you are incorrect. HIPPA protects the privacy of medical records.
HIPAA applies to any medical information but does not apply to whether you have been vaccinated or not. Only way it would come into play would be if you claimed a medical reason for not being vaccinated and then only to how much information doctor would have to disclose. But it does not protect from disclosure of vaccination.
Similarly, it doesn't protect you from having to disclose if you test positive which would put other employees at risk nor from you being required to test and having to disclose results to your employer.