Yes, it is very interesting, since when he was on earth he was annointed (at the time of his baptism _ Mat. 3.16,17; Luke 4:17-21), and the rest is as you say ... which shows that the holy spirit is not a person as many think, or otherwise, how is it explained that this "person" was already with him even after he was resurrected and before he ascended to heaven, and then there he has to receive it again from the Father?
John 20:22 And after he said this he blew upon them and said to them: “Receive holy spirit. ..."
Luke 24:49 "And, look! I am sending forth upon YOU that which is promised by my Father. YOU, though, abide in the city until YOU become clothed with power from on high.”
Acts 1:4 While he was meeting with them, he ordered them: “Do not leave Jerusalem, but keep waiting for what the Father has promised, about which you heard from me ..."
... 2:4 and they all became filled with holy spirit and started to speak in different languages, just as the spirit enabled them to speak.
As can be seen, his disciples had to wait to receive holy spirit from heaven, which occurred on the feast of Pentecost, on Sivan 6, 50 days after the resurrection of Jesus. If the holy spirit were a person, did "he" go to heaven with Jesus, and then came back because of a request that Jesus made to God?