"State" in that context clearly refers to foreign nations (states) not states as in The United States Of America. Foreign power is distinct because it would refer to things like governments-in-exile or perhaps resistance groups.
It seems to me that it states “with another State”, as in a capital S State or a member State of the United States. Then explicitly calls out as another option, “or with a foreign power”.
Furthermore, the title of Article I, Section 10 of the US Constitution is “Powers Prohibited of States”.