Neil Patrick Harris is actually a version of The Architect trying to unlock some secret code buried in Neo's mind that will end the resurrections of The One.. So he makes himself appear as a therapist, trying to probe his thoughts for the clues. Creating a personal Matrix in order to use the information on the real Matrix. Trinity and Neo died in the machine city, hence why they're in this faux Matrix and why Morpheus is not there. He is alive and in Zion. The machines took Neo and Trinity's bodies because something about their connection in the key. They keep finding each other in these resurrections.
I'm just spitballing here