John 4:24 “God is spirit, and and His worshipers must worship Him in spirit and in truth.”
Orthodox Trinitarian Christians do not have this modalistic view you seem to have that the Holy Spirit is the spirit part of God. The Holy Spirit is a PERSON not just the spirit portion of God.
The teaching that God is spirit is one of the most fundamental teachings of orthodox Christianity. What is true is that the Bible speaks of the “spirit of God” and since God doesn’t have body and spirit parts, this is taken to mean the Holy Spirit.
Now if you are Mormon, then you would believe differently that God the Father has a body. But even in that case the Holy Spirit is a separate person which happens not to have a body and is not just the spirit portion of God.