Can a State impose more restrictive screening for certain States that

I think NY did too and later they treated neighboring states differently.

"What is, is legal" isn't all that useful. The restrictions were short-lived; anybody who would have tried to get standing to contest them would have quickly found their cases tossed as moot when the restrictions were lifted. Short-term injunctions might have been granted, but showing sufficient loss to merit an injunction would have been difficult.

There was differential outrage and indignation here when one state imposed restrictions (or required quarantine, hardly enforced on the traveler), and justification when another state, for the same reason, imposed the same restrictions. So attitudes and from-the-hip responses are sketchy.

There's some Federal case law guaranteeing freedom of travel between states; it was a right given in the Articles of Confederation, not in the Constitution (but then again, most assume it was deemed unnecessary given the tighter relationship between states). I'd argue that it would be a right assumed since guaranteeing natural rights by not limiting them was what the Constitution was all about, with the Bill of Rights deemed a mere spelling out of some of the more prominent rights that a citizen had by virtue of being a human (with all due caveats for limitations on women and the not-free or unpropertied), which the government didn't provide but merely was to not limit. But all rights are subject to "compelling state interest" restrictions.

Courts have been hesitant to overrule restrictions on travel or commerce when they involve public health, and for that there are a number of cases. As long as the travel restriction was based on established state interest and based on reasonable criteria, limited in time and extent, then I doubt a judge would do more than toss out the case.

They did not say that people , could not come, but from most states, but a 14 day quarantine even for returning Vermonters, was required or the results of a negative test after arriving. This was first waived if fully vaccinated.

Friends who recently went to Hawaii needed tests before they could get on the plane to Hawaii - even though fully vaccinated. I think that just ended.

As to if these regulations were legal, I read nothing on them being successfully challenged.

Especially in the case of a public health emergency.

Obviously that isn't blocking people from a particular state, but would seem to be comparable.

there. I don't know if they were very successful or not, I kind of doubt it.