Why is there no mention of the man's soul?
1 Cor 5 >
Yes, here Paul says
"absent in body but present in spirit" > in 1 Corinthnians 5:3 >
He does not mention his own soul.
And later he talks about their being "along with my spirit", in 1 Corinthians 5:4.
And then Paul says to deliver the man "to Satan for the destruction of the flesh, that his spirit may one saved in the day of the Lord Jesus." (in 1 Corinthians 5:5).
So, here, there is no mention of saving the man's "soul".
But if the soul is spiritual, then it is reasonable that it is part of your spirit. My opinion is our soul is the realm of our spirit which experiences. It is the conscious part of our spirit. So, our soul includes the part of our spirit which can feel what is going on in our bodies. And our soul includes our spirit which is experiencing our connection with God in His love and sensing how God in us is leading us . . . "moving" us.
"But he who is joined to the Lord is one spirit with Him." (1 Corinthians 6:17)
The problem with that guy was he was seeking to experience the physical pleasure he could have with his father's wife. So, his spirit needed connection with God in God's almighty power and immunity against evil feelings and desires and preferences. By being "one spirit with Him", the man would more and more share with God in God's character of love. And this would affect his soul . . . with soul's experience of feelings and emotions and desires and preferences. In actual union with God, God would share with the man how Jesus is and loves. And his conscious spirit . . . his soul, in my opinion . . . would then experience how God is in His love > more and more as he grew in this.