Sovereign, yes, but not like a country.
Let’s remember how the US Constitution begins:
It does not begin with “We the several states, in order to form a federation.” Yes states have sovereignty, but the Constitution never puts state sovereignty above the sovereignty of the nation as a whole; it is written to the benefit of the people of the Union as a whole. We fought a civil war over that.
State sovereignty is separate from federal sovereignty. The constitution was written giving only certain enumerated powers to the national government. Things such as making war, issuing money, regulating interstate commerce, making treaties with foreign nations. In all other matters, the power was granted to the sovereign states. For example, building construction codes, state and local police, criminal and civil law, zoning, speed limits, actually most of the rules and regulations we live by daily come from state and local jurisdiction.
State rights vs. federal authority have always been points of disagreement. States sue the feds and vice versa. The Supreme Court has often been called on to referee whether states have jurisdiction over an issue, or the national (federal) government does.. Probably the most visible of these today is legalizing marijuana. There are federal laws against this. Yet, a few states, claiming state rights, have made it legal in their states. For now, the Feds are looking the other way and ignoring most enforcement. But if a president decides to enforce the federal law and stop states from selling pot, it will surely go to the Supreme Court. They will have to decide which sovereign (the feds or the states) have authority over the issue.
Here's a good article explaining states rights.
"In American political discourse, states' rights are political powers held for the state governments rather than the federal government according to the United States Constitution, reflecting especially the enumerated powers of Congress and the Tenth Amendment. The enumerated powers that are listed in the Constitution include exclusive federal powers, as well as concurrent powers that are shared with the states, and all of those powers are contrasted with the reserved powers—also called states' rights—that only the states possess.[1][2]"https://en.wikipedia.org/wiki/States%27_rights