In the ancient world, and in the world of the early Christians, we need to remember this. Prestige was associated with oral literature first, and with written literature only second. Learning was training the memory first, and the ars memoriae of locative memory and memory palaces.
In most traditional societies, it’s common to start learning bits of long epic poems at preschool ages, when kids don’t even understand the words of the archaic language they’re learning to recite or sing. They are directly exposed to all the rhetorical devices that aid memory, even when they just understand the sounds of them.
And of course, the early Christian Papias, who is known to have been mentored by some of Paul’s cousins who were female physicians, and ran a free clinic but sponsored the building of three monasteries, said outright that he preferred learning the teaching of Jesus and the apostles from people who had heard them preach, and not from books.
(Although his huge book of written reminiscences of eyewitness testimony has almost entirely been lost to us. Which shows the problem with relying on oral or written testimony.)
So it makes perfect sense that Paul (or whoever, or Paul’s team helping him) would compose a speech or series of speeches with more formal Greek and more rhetorical devices than he would use in a mere letter.