Many republics (including Singapore) do not have "states", so clearly "states rights" is not "a fundamental construct of a republic".

Nobody sane has ever cared about "states' rights" consistently - it's a silly concerpt. It was invented as part of the Lost Cause mythology to justify secession. (Fugitive slave laws, which are pretty antithetical to 'states rights," were very much something the antebellum South pushed for.)

The distinction is "threat to any government" vs "threats to OUR government"

Sure, ANY Republic does not rely on States, as evidenced by Singapore. But OURS (if you are also a USA citizen) does.

you are correct that I should have stated "our republic" not all republics.

That said, the idea that "states rights" originated after the civil war is absurd on face vale. Powers and autonomy left to the states are evident in our founding documentation, and obviously present in the lead up to the civil war as well.

The idea that a centralized government leaves no powers to the state and local level is a silly concept and counterfactual. It is obvious in the interstate commerce clause and many other parts of the constitution.

That the US started out as a federation of independent states is a given. My point is that "states' rights" as a political-moral philosophy doesn't make much sense, and almost nobody has pushed for states's rights consistently or when it goes against what they otherwise want. One might argue that decisions should be made at the smallest (most local) level that makes sense, but the idea that "state" means "local decision-making" is pretty dubious. Furthermore, "states' rights" as a political rallying cry in the US came after the Civil War and was used to justify segregation.