Did Paul ever write about the trinity in his letters? If not, why?

I am sure that those who are obsessed with promoting the doctrine scour the scriptures regularly to find even some little hint of it anywhere they can.

Paul wrote clearly and carefully so that many would not misunderstand anything that he wrote. The following are some of the things that he wrote:

“May the God who gives endurance and encouragement give you the same attitude of mind toward each other that Christ Jesus had, so that with one mind and one voice you may glorify the God and Father of our Lord Jesus Christ.” - Romans 15:5–6

“But I want you to realize that the head of every man is Christ, and the head of the woman is man, and the head of Christ is God.” - 1 Corinthians 11:3

““one Lord, one faith, one baptism, one God and Father of all, who is over all and through all and in all.” - Ephesians 4:5–6

“For there is one God and one mediator between God and mankind, the man Christ Jesus,” - 1 Timothy 2:5

Talking about Jesus, Paul said: “He is the image of the invisible God, the firstborn of all creation.” - Colossians 1:15 (KJV, ESV, ASV and many more Bible versions)

“For God is not a God of confusion but of peace.” - 1 Corinthians 14:33

Of course, Paul wrote in ancient Greek and the Greek can be messed with and the above verses can be twisted to promote any false doctrine.