You write, “It is the NSA machine side that records everything about us.” And in the next sentence you add what everyone believes, “The human side needs a court warrant to listen in on us if we are domestic based.”
Realistically, if the NSA has recorded our calls they can hold those calls until Gabriel sounds his trumpet or Big Brother gets nosey; and nosey it is right now as it digs through Secret Service calls that occurred around January 6.
The machines record without human involvement 24/7 everywhere. They are always on.
If NSA humans listen or watch the recordings, it is done by warrant for US persons inside US jurisdictions. For all other persons, a warrant is not needed.
US persons inside US jurisdictions have protections by law.