Have we ever had anything like vaccine passports before anywhere around the world?

I'm going to take a crack at this even though I don't have a PhD in this, because it's been about a day since you asked and I did recently attend an Oxford lecture on the topic, given by Troels Arbøll. Hopefully my notes will be of use to you.

Troels Arbøll is an expert on "medicine, magic, and the transmission of knowledge in the Middle East" and the topic of the lecture I attended was Ancient Mesopotamian epidemics.

Frank M. Snowden once said "Epidemics facilitate historical development and change, they're useful for understanding social and religious changes as well as the outcome of wars." They're considered the currents beneath the surface of history, because they drive so much of people moving and so much economic crises.

Mesopotamia — Babylonia in the south, Assyria in the north — has a bunch of tablets with references to epidemics and diseases, mostly dating from 1900 BCE onwards. For example, "simmum" is a skin eruption disease, "di'u" is a disease that causes headaches, and "mutanu" is the term for "lots of death in a time of crisis" — famine, epidemic, whatever.

Ancient Mesopotamians treated diseases with a combination of medicinal treatments with prayer and rituals. In the first millennium BCE, they didn't really differentiate between magic and medicine. Physicians did have knowledge we'd consider real medicine, they were specialists and the most highly regarded socially. They performed surgery and used pharmaceutical knowledge. Exorcists were connected to temples, serving as healing staff. There was not widely available healthcare. It's not clear that they treated regular people or the lower classes, but folk healers aren't attested to by the written sources (which doesn't mean they didn't exist).

Large-scale crises like city-wide epidemics were considered to be chaotic and impersonal and to be the responsibility of "large cosmic events." Still, we have records of letters from the king of Lebanon from the king of Egypt, asking for details about a plague:

Inasmuch as you say 'I will not permit the men of the town of Sumer to enter my city; there is a plague in the town of Sumer.' Is it a plague against men or against asses?

There were political reasons for the kings to care about epidemics. We have reports from advisors to kings about different regions and cities in the county that were stricken with disease. There were definitely letters and chronicles that mention epidemics, but unfortunately they tend to be isolated and one-sided; we don't have responses to the letters.

Regardless, we know that palace epidemics resulted in social distancing and isolation being ordered. If a woman got sick in a particular way, they knew not to have anyone sleep in her bed, drink from her cup, or sit in a chair she used. They knew about contagiousness, lit. "The wound that makes itself be accepted by others."

Epidemics were viewed as cyclical events, like typhoons or monsoon winds or moon phases (or flu season). In the first millennium BCE, though, there were rituals anticipating them. These rituals were "good for" a year (much like modern vaccines) and were represented by figurines in houses that might literally say something like "disease, di'u-illness, distress, and epidemic will not come near the man or his house for one year."

Also, folks back then knew to avoid sharing driving vessels, chairs, and beds with infected people during an epidemic, they burned or fumigated personal objects, and avoided infected cities.

On the flip side of your question, rituals designed to expel demons may have marked homes as infected, the magic meant to enclose a quarantined patient but also served as a warning to other people that there was sickness and that they should avoid it. This may have only been for the elite; we don't know. Even back then, it could be hard to keep isolated when you're poor and need to go to work.