Correct spelling is "kainos".
2 Corinthians 3:6 KJV
Who also hath made us able ministers of the new testament; not of the letter, but of the spirit: for the letter killeth, but the spirit giveth life.
Every English Bible version translates "kainos" in this verse as "new", not as "fresh".
That is the problem as it is not presenting the right context of what has been written in the Greek text.
You quoted 2 Cor 3.6 and it highlights how by translating "Kainos" as simply "new" it has reinforced that God is not the same yesterday, today or tomorrow however if it is translated as "refreshed" the three times this Greek Root word is imbedded three times in the Greek word "καινῆς", showing that the silent and unwritten "Salvation Covenant" has been refreshed.
In Jer 31:31ff God will not make a "Brand New" covenant with the nation but that He will rather refresh the Kingdom of Priests, a Holy Nation and His Possession among the Nations Covenant which He had initially made with the nation of Israel at Mt. Sinai. The text in Jer 31 makes this plainly clear.
Sadly, many Christians want a "Brand New Covenant" that no longer ties any covenant that God may have made, or will make, with the nation of Israel, with respect to their relationship with God. They are mistaken and their theology condemns them..
Jesus said the something similar in Mat 13:52.
The Salvation Covenant has not been changed, however, the process by which it will now be administrated has. Know what I mean?