I suspect this public discussion about the authoritarian tendencies is fake and the introduction of 'papers' is looming because businesses here and elsewhere want it. It's the economy ...
It's an internal and external issue.
As for the travel between countries ... for the last handful of decades one already had the need for vaccination papers if one travels to the third world etc. either from the employers or from the countries that you visit, as I can personally testify. It will be interesting to see how this pans out in each country.
No doubt the airlines would like to have these covid passports upfront i.e. before travel, to make it easier for them.
We already have our NHS records in the hands of the US corporations, if anyone cared to notice.