Why are you troubled, and why do doubts arise in your hearts? See My hands and My feet, that it is I Myself; touch Me and see, for a spirit does not have flesh and bones as you see that I have.
No, scripture does not call the resurrection body spiritual
Psyche doesn't have any physical connotations to it, on the most literal level it means breath; it refers to the living energy or essence of things in the world.
Pneuma is used throughout the new testament to refer to the holy spirit, so in saying that this is a soma pneumatikon, he's saying that the new body is filled with the Holy spirit, while the old body, the soma psychikon, had the energy and essence of the things in this world.
The old body is human (Psyche). While the new body is spiritual. (Pneuma)
The Bible defines the soul as the mind, will, and emotions. The Bible also tells us that as a baby up to and through the time He was a man Jesus had to learn and grow. He didn't know everything as a man. He had a finite and limited mind. This was His human soul. This is the soul that would die as He was nailed to the cross. The Bible is pretty clear that Jesus died for sinners. As God, Jesus didn't have to learn and grow. He was infinite in wisdom and knowledge. This is His Divine soul. This is what entered His new body when He was resurrected. The finite human soul has perished. The Divine soul lives forever.