So HIPPA only prohibits medical providers (hospitals, physicians, pharmacies, etc) from disclosing your medical information to third parties except for specific reasons (your doctor sending records to a surgeon for an upcoming surgery for instance) or unless you authorize the disclosure.

HIPPA wouldn’t restrict a restaurant from requiring you to confirm you were vaccinated. If you didn’t want to share, then the restaurant has the right to refuse you entry (unless some local law would apply).

Now, I think the bigger question you should be asking is the legality behind hospitals sending your information into the CDC database once you get vaccinated.