[FredZarguna]

It requires state legislatures/executives/judicials to be bound by an oath.

That doesn't mean the oath has to be part of their respective Constitutions. As a matter of fact, because of the Supremacy Clause, they're already required to take the oath by the US Constitution, and no further further Constitutional or statutory provision is required.

[donmeaker]

You nailed it. Congrats!