You correctly note that it is God that is speaking, not that he is being addressed. So then when the expression "God, thy God," showing that the one addressed is not the Most High God but is a worshiper of that God.
The question should be, why did God/Father called His Son, God, if He is not God? And in Exodus 20:3 it says, “You shall have no other/different gods before me.” And in Acts 7:55-56 Stephen saw the “Lord Jesus Christ standing at the right hand of God.”
Read Psalm 110:1 and Matthew 22:44 “the Lord said to my Lord: “Sit at my right hand until I put your enemies under your feet.””
Now, who could sit right next to God/Father? Other/Different/heteros god/s? NO! Only God can sit next to God. No created beings can sit next to the Creator/God.
Hence it becomes irreconcilable IMO to equate Jesus with the most high God, when Jesus has a God over him, and is subject to that one.
That’s why you need to understand John 1:1a, 1:1b and 1:1c, because according to John 1:1 the Lord Jesus Christ is God and not an “a god”.
1CO 15:28 When all things are subjected to Him, then the Son Himself also will be subjected to the One who subjected all things to Him, so that God may be all in all.
Here we have the Son, i.e., the Lord Jesus Christ, and “the ONE who subjected all things to Him”, i.e., the God/Father. Does this mean He is not God? NO!
Verse 28 is after all, including death –1Co 15:26, was subjected under the Lord Jesus Christ’s feet.
And “then comes the end –1Co 15:24”, “at His [2nd] coming –1Co 15:23”, where there is no more sequence like the one in verse 23, “when He hands over the kingdom to the God and Father –1Co 15:24” and “then the Son Himself also will be subjected to the One who subjected all things to Him –1Co 15:28”.
From the start of the Creation, i.e., “All things came into being through Him, and apart from Him nothing came into being that has come into being. –John 1:3, Col 1:16”, to the Redemption of men, i.e., the Lord Jesus Christ’s earthly ministry, to His death on the cross, to His burial, to His resurrection, and to His ascension to the right hand of God, all these are Christ’s mediatorship between God and men. IOW, at the end –1Co 15:24, at His 2nd Coming –1Co 15:23, His office, as the MEDIATOR [from the start of the creation to the redemption of men], between God and men ends or no longer needed. All works that were laid under His feet, from creation to death, is finish. No need to intercede between God and men for they are all will be with God at end, because there is no more enemy to defeat or “DEATH IS SWALLOWED UP IN VICTORY”.
“The last enemy that will be abolished is death. -1Cor 15:26”