[ubernostrum]

Spying and other intelligence gathering was, at the time, seen as a "necessary and proper" part of running a military. And the Constitution explicitly authorizes providing for "the common defense", explicitly authorizes the existence of military forces, and grants the power to make laws "necessary and proper" to carrying out these authorizations.

Spying and intelligence are still, in the present day, seen as a matter of national defense. NSA is explicitly under the Department of Defense, for example. CIA is civilian, but is still framed as serving a defense/national security purpose (thus Constitutionally justifiable) and scoped to be foreign-facing (domestic intelligence is primarily the FBI's province, "necessary and proper" for enforcing federal law).