The Trinity is not defined in Scripture however. Just like the Incarnation isn’t defined in Scripture. People have interpreted verses that show these concepts differently however. (and I agree with you because they are in Scripture)
But private interpretation doesn’t work.
Incarnation:
John 1
1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was with God in the beginning. 3 Through him all things were made; without him nothing was made that has been made. 4 In him was life, and that life was the light of all mankind.
…
14 The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.
15 (John testified concerning him. He cried out, saying, “This is the one I spoke about when I said, ‘He who comes after me has surpassed me because he was before me.’”) 16 Out of his fullness we have all received grace in place of grace already given. 17 For the law was given through Moses; grace and truth came through Jesus Christ.
Philippians 2
6 Who, being in very nature God,
did not consider equality with God something to be used to his own advantage;
7 rather, he made himself nothing
by taking the very nature of a servant,
being made in human likeness.
8 And being found in appearance as a man,
he humbled himself
by becoming obedient to death—
even death on a cross!
9 Therefore God exalted him to the highest place
and gave him the name that is above every name,
10 that at the name of Jesus every knee should bow,
in heaven and on earth and under the earth,
11 and every tongue acknowledge that Jesus Christ is Lord,
to the glory of God the Father.
The above also shows the relationship between the Father and Son.
I have seen in the past the hang up for Catholics is knowing the Holy Spirit is GOD through Scripture:
Acts 5
3 Then Peter said, “Ananias, how is it that Satan has so filled your heart that you have lied to the Holy Spirit and have kept for yourself some of the money you received for the land? 4 Didn’t it belong to you before it was sold? And after it was sold, wasn’t the money at your disposal? What made you think of doing such a thing? You have not lied just to human beings but to God.”
We see in Scripture that Jesus always called the Holy Spirit a him and not an it- so a person or being with a separate identity yet still the very GOD. We also know that it is the Father that sends the Holy Spirit to us and Jesus:
Acts 2
33 … he has received from the Father the promised Holy Spirit …
Do you need me to list all the verses that support the idea that the Father is GOD, Jesus is GOD?