Same one you cited.
Try looking at Article I, Section 8, Clause 3, for example.
Yep...Congress determines IF war is declared, issues letters of marque, determines how seized items are dispossesed, code of discipline for members of the military.
The closest to being contrary to what I said is "To define and punish piracies and felonies committed on the high seas, and offenses against the law of nations;"
"Clause 3: To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes; " is what happens here, not there.
Also, I would be interested to know which portion of Article II grants "authority to manage foreign affairs".
I'll concede my shorthand was over-broad here, however:
Section 2. The President shall be commander in chief of the Army and Navy of the United States,...
Clause 2: He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur;...
...he shall receive Ambassadors and other public Ministers;...
The Legislature (Congress) passes laws - within its authorizations and not violating the Constitutionally directed Executive powers - and the Executive manages the details of foreign affairs. Congress may not run the details of the military's actions (such that it can be said to be "commanding"), nor receive Ambassadors, nor negotiate Treaties.
Regardless - and dealing with the issue at hand - the Federal Government is the only agent authorized to deal with foreign powers on behalf the nation - and it is authorized. It is also authorized to deal with foreign individuals on behalf the nation. Furthermore, there are pretty clear lines drawn between foreign locations, territories, and domestic locations - and what powers are given.