Yes, he is holy spirit now. John 1:1. He is not flesh in any way because the perishable cannot inherit the imperishable.
John 1:14, 2Corinthians 4:6, Hebrews 1:3
After Jesus resurrection He appeared first to Mary and told her not to touch Him yet because He hadn't ascended to His Father...
John 20 (NKJV)
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¹⁵ Jesus said to her, "Woman, why are you weeping? Whom are you seeking?" She, supposing Him to be the gardener, said to Him, "Sir, if You have carried Him away, tell me where You have laid Him, and I will take Him away."
¹⁶ Jesus said to her, "Mary!" She turned and said to Him, "Rabboni!" (which is to say, Teacher).
¹⁷ Jesus said to her, "Do not cling to Me, for I have not yet ascended to My Father; but go to My brethren and say to them, 'I am ascending to My Father and your Father, and to My God and your God.' "
Then He appeared to the disciples and taught them for another 40 days.....eating, drinking, and fellowshipping with them.
He let doubting Thomas put his finger in His side where He was pierced...
When He was taken up it was His glorified body...