How would they be used?
Even if it is called a Passport, it will not look like what all of us have in mind when thinking of one. The paper version of it probably will not exist at all, but rather it will be in the form of a mobile app with a barcode or QR code, that will be scanned by the border officer and it will show your vaccination status.
There are rumors of them containing more information other than that, like travel restrictions for the country of destination, them holding other medical information, and maybe the status of your last COVID test. There are talks about paper versions for people who do not own smartphones too, but at the same time, it raises a lot of questions of how easily it could be forged.
The best option would be to link the profile to a database, but in the United States, the vaccination data is not stored at a federal level, but at a state one. There could be problems with linking the databases, as well as numerous safety concerns.
Do they exist now?
In the form described earlier, the answer would be no. They do not exist in that form, be it as an app or in paper form. The closest to it that other countries have gotten are Israel’s “Green Passport” which is an app that stores your vaccination status and issues a scannable QR code and the European Union’s EU Digital COVID Certificate. Both of them have been shown to be quite effective, the EU Digital Pass allowing people to cross borders faster and allowing less strict restrictions on what citizens do, as it allows easier checking of vaccination status.
Even here at home, there is something akin to a COVID passport, New York state has the Excelsior App, which shows either proof of vaccination or negative COVID-19 test. Yet, this app is not used anywhere else outside the state of New York, and it has its drawbacks as it does not easily recognize vaccinated status from outside its own database or the ones in New Jersey or Vermont.
Would all vaccines qualify?
Unfortunately, it does not seem like they would. Based on the aforementioned versions that are currently in use, only the BioNTech and Pfizer, Moderna, AstraZeneca, and Janssen Pharmaceutica NV are approved for the EU Certificate, with the Janssen Pharmaceutica NV being added later than the first ones.