> “terrorism” originally exclusively denoted action by the State against its own subjects

Correct, in the French Revolution, I believe. There are a variety of definitions of terrorism. The common elements seem to be the (a) peacetime use (b) of violence (c) against non-combatants (d) as a political tool. There also seems to be an unspoken requirement that it occurred after the formation of modern states (otherwise almost all of the preceding human history was terrorism and the word gets normalized); the French Revolution is a useful line.

The NSA targets non-combatants (c) in peacetime (a). It does not use violence (b), though it does enable it (⅓b). It does not do so for domestic political aims (to any proven degree); the degree to which it does so abroad depends on where one draws the line between politics and geopolitics. (The CIA, in contrast, engages in all four overseas.)

When an organization that has done terrorism becomes a terrorist organization is another question.

Okay that settles it, the word terrorism has so many conflicting and overlapping contexts that it is useless