Local ordinances for San Francisco, Los Angeles and NYC allow for customers to produce proof of vaccination from their jurisdiction of issuance and they kept it vague. I think they realize that not everybody visiting will have the CDC covid 19 vaccination card, but if anything, these will be templates for future local ordinances across the country. Jurisdictions are issuing their own proofs of vaccination so it isn't really practical specify which ones will be valid.

Don't bother wasting time thinking about it, just bring what you have and enjoy yourself.

If you want to take a side trip to Canada, then any record of your vaccination must be translated into English or French.