This is about the soft sciences of biblical criticism and analysis on Hebrews and Psalms

So in Hebrews the author makes a claim of God the father speaking about his son, Jesus Christ showcasing how he talked to the son vs the angels.

Hebrews 1:5-9
New American Standard Bible
5 For to which of the angels did He ever say,

“You are My Son,
Today I have fathered You”?
And again,

“I will be a Father to Him
And He will be a Son to Me”?
6 And when He again brings the firstborn into the world, He says,

“And let all the angels of God worship Him.”
7 And regarding the angels He says,

“He makes His angels winds,
And His ministers a flame of fire.”
8 But regarding the Son He says,

“Your throne, God, is forever and ever,
And the scepter of righteousness is the scepter of His kingdom.
9 You have loved righteousness and hated lawlessness;
Therefore God, Your God, has anointed You
With the oil of joy above Your companions.”

The lines that are being quoted comes from Psalms 45:7
Psalm 45:7
New American Standard Bible
7 You have loved righteousness and hated wickedness;
Therefore God, Your God, has anointed You
With the oil of joy above Your companions.

But this psalms seems to be about this.
A Song Celebrating the King’s Marriage.

For the music director; according to the Shoshannim. A Maskil of the sons of Korah. A Song of Love.

So it does not really seem like it’s about God speaking to anyone. What’s the logical process to connect those dots? Is it the part where it says “ Therefore God , your God”? Is that implying somehow God speaking to God?