In the end it will be a federal mandate that these businesses use these passports. And there will be a tax associated with it.
Very easy to counterfeit
A government mandate creates a legal problem because SCOTUS already ruled that the government cannot force you to get vaccinated. That is why they need cooperation from the private sector. But that also opens up some legal issues many small business will not want to take on. If local small businesses have protection from the state, they will not participate. Amazon can afford to lose a few million customers, small businesses cannot afford to lose a hundred customers.
They use the Yellow Fever Vac as an example. It is not the USA that requires the yellow fever vac it is the country you are visiting that requires it for entry. Also the yellow fever vac went through the full trials and is not only approved for Emergency Use like all of the COVID vacs.