True. They are three persons and can interact.
True. They are one God.
You need to look at ALL verses of Scripture and find the one understanding that matches them ALL.
I have shown you many more verses that require the Father, Son, and Holy Spirit to be One.
The standard concept of Trinity is based on harmonizing ALL verses. It is the only understanding that fits ALL the data.

So the doctrine of the Trinity can easily explain John 17:1 but your non-trinity understanding cannot explain, for example, Isaiah 9:6.