What about Legislative jurisdiction as defined in the Constitution?
Article 1, Section 8 [POWERS OF CONGRESS]
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of Particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings
I’m not an attorney but that seems to establish Federal jurisdiction over DC and lets it buy land for military bases (usually in places nobody can use for much like the pine barrens of Georgia and the Carolinas).
That really doesn’t seem to have much to do with Congress being able to declare war or having treaties supersede the constitution.