The Federal government was never meant to be “supreme” over the states. The states after leaving Britain had had their fill of large oppressive and supreme government, and wanted a government that was limited. So they delegated express powers to it. You don’t delegate powers to a superior, only to inferiors or equals. At best the Federal government is the equal of the states, not the master of the states. It may be said to be “supreme” in the areas of power delegated to it, but only in those, and only so long as it is governing at the consent of the governed. The states also hold supreme power in all the numerous areas in which they reserved power.
When referring to the sovereign states, I am referring to the citizens of the state collectively.
That definition applies equally well to the concept of the federal "state".
The Framers instituted the concept of dual sovereignty as a system of shared authority between federal and state governments with each sovereign checking the other. As with the concept of shared powers between the three branches of federal government it was designed to provide balance between the interests of the state sovereigns and the federal sovereign.
Here's a simple test. Let's see who is subordinate and who is supreme:
Suppose the state of Arizona wants to declare war on Mexico (I can't that I would blame them). Do they have an unfettered right to proceed?
Let's say that the state of Tennessee has gotten tired of mitigating flood damage from the Mississippi River and starts building embankments that ensures that any flood waters will drain into Arkansas instead. Who would be the final arbiter of that dispute?
The state of Illinois decides that they want to aggregate more power so they devise a scheme to subdivide their state into three pieces. Can they of their own volition complete this action?
In each of these examples there is an authority that is superior to that of the individual states. The agents of that authority are divided between the President, Congress, and the Judicial branch of the federal government. I recognize that it is problematic, especially with the chronic desire of leftists toward overreach. And you are correct that the intent was for balance between the sovereigns, but with the power of the federal sovereign being divided among the representatives of the individual states.
The Federal government was never meant to be “supreme” over the states
The United States Constitution, Article Six, Clause 2 says otherwise:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.