I invite any constitutional lawyers to opine here.
It appears to me that in the U.S., any law, or agency regulation or rule which alleged authority to require a citizen or their employer to reveal their vax status, and alleged a penalty, fee or crime if this information is not reported, is effectively defeased by the 5th amendment to the U.S. Constitution. In that amendment, a citizen cannot be compelled to incriminate themself. By extension then, any law, regulation or rule alleging requirement of a travel passport, vax passport etc. is also defeased.
As an adjunct constitutional argument, the 1st amendment states that ‘no law shall be passed prohibiting the free exercise of religion or abridging the freedom of speech or press.’ Freedom of speech includes the right to remain silent. ‘You have a right to remain silent. And anything you say can and will be used against you.’ For example, you have a right to not report vax status or other parts of personal health. By logical extension then, an employer or agency of government cannot be compelled by law, regulation or rule to require an employee to report their vax status.