Only sovereign states can ratify treaties, yet the 50 states are barred from conducting foreign affairs. The United States, on the other hand, has ratified treaties. You're actually describing the European Union, which may negotiate jointly but ultimately treaties are ratified by the member states.
The civil war pretty well put to rest the idea that the idea that the states are truly sovereign. They may have been before they signed the constitution, but today there isn't even a way for a state to leave the union (we have no Clarity Act). I don't see how a state in such a situation could possibly be considered remotely sovereign.
Also, a republic is merely a type of government. The legal status of the states would not really be different if the U.S. were a direct democracy, a monarchy, or an empire. We're a union of 50 states, which happens to be governed as a presidential republic.