They won't need paper vaccination passports to see who got the "vaccine". Under HIPPA "patient portability" of the Kennedy-Kassebaum Act under Clinton & the 104th Congress, then furthered under Obama Care, it's already transmitted to your permanent electronic healthcare records (ERH).
When I came down with CV-19 last November, I got a letter (4 months later!) from the county health department informing me I had the virus & needed to follow quarantine protocols. So no true HIPPA or ERH privacy. The EU is doing better on PII that the USA. Especially in the area of misuse & data breeches & other nefarious reasons.