> If it is the U.S., then obviously no, the NSA is an arm of the state.
Its perhaps worth noting that “terrorism” originally exclusively denoted action by the State against its own subjects, though it was within a few years expanded to include other activities.
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.
Some here in the states don't exactly feel like the people running the USG have the people's best interests at heart. Common folk across countries probably have more in common with each other than with the ruling elite.
State-sponsored terrorism is a thing - and has been for a LONG time. And US citizens are targets as well as non-citizens.
Nothing about US foreign policy suggests that. Very little about the Federal government’s domestic policy does.
This statement needs the "we" defined to be meaningful.
If it is the U.S., then obviously no, the NSA is an arm of the state. If "we"` is e.g. China, probably no, because words have meanings and the arms of recognized foreign states don't conduct terrorism, they do espionage and they do war. If "we" is a freshman dorm room, then, of course, the NSA is a terrorist organization alongside the student government.