Of course, the Supremacy Clause prevents the regions from applying laws that contradict the Constitution. But regional laws that violate the Bill of Rights do not contradict the Constitution.
In Barron v. Baltimore, John Marshall said that the People adopted the Bill of Rights "for their own government, and not for the government of the individual States." He said that "no limitation of the action of [the federal] government ... would apply to the State government," and that any provision, "however comprehensive its language, contains no restriction on State legislation," unless it is specifically provided that a state shall be so restrained.
So, yes, the Supremacy Clause prevents a state from violating the Constitution. But a region denying freedom of speech, or gun rights, does not violate the Constitution. As it currently stands, the Bill of Rights is a restriction on federal, not regional power.
I am familiar with the case you quote and if the Supreme Court of Atlasia would apply it as such, then it would be relevant.
Fact remains is that this is Atlasia, not the United States. However correct that John Marshall's words are, the thrust behind the ruling might not be viewed as correct by the present Supreme Court.
We have not yet had any rulings in front of the Supreme Court that challenged Article VI, so henceforth our precedent in Atlasian jurisprudence is rather thin, and there is nothing that says that Marshall's words would apply here.
In addition, the context in which the Atlasian "Bill of Rights" was adopted differs from the United States. In the United States, the Bill of Rights was a last minute addition to the Constitution, which formed ten amendments. In Atlasia, the so-called "Bill of Rights", Article VI, was adopted immediately as necessary within the Constitution and forms a vital part of it.
Also, the wording of the Amendments differs, to a great enough extent to where words could easily be interpreted to mean both Regional and Federal governments.
For example, in the United States, the reading of Amendment I is, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press, or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."
In Atlasia, the corresponding Article VI, Clause 1 reads, "No agency of government shall make any law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."
Whereas in the American version, the wording is clear as to apply to Congress, in the Atlasian version, the wording is more vague. Must an agency of government be only federal or can it also apply to the Regions, who certainly have agencies of government.
The Supreme Court would have to rule as to exactly what an "agency of government" is in order for us to get a better understanding of where exactly Article VI applies in the federal government and the Regions.
With the lack of relevant precedent, my opinion is that we take the cautious road, instead of the lackadaisical one. When a case arrives before the Supreme Court that challenges the application of the Bill of Rights on a Regional level, then and only then should we decide how to amend our Constitution to fit the parameters of that ruling and its decision, if need be.
If we pass such a general and overarching amendment such as the one presently before us, we risk the law of unintended consequences creating more problems than we can solve and giving the Supreme Court greater leverage to impose its own ideals of what violates the clause over us.