>>I assume
Your assumption is wrong because the direction is wrong. If one reads Plato’s Republic/Symposium/Dialogues etc, he uses inductive thinking to try to identify what God is.
Paganism has pre-defined gods that are worshiped in established ways.
The only similarity that Platonic philosophy has with Christianity is the number 3. Well, Plato happens to love the number 3 - there are three elements of the ideal society in the ‘Republic’, there is the tripartide soul, there are his three levels of reality. He loves the number three. Does it have to do with the Trinity? No.
I said at its root “pagan” means folksy. Whatever Plato was, that’s not it. He was a citydweller, an academic, and had aristocratic airs. Peasants don’t go around dreaming up their own philosophical systems, obviously. But you must admit people use the term in more ways than that. In addition to “pre-defined gods...worshipped in established ways” it also has the connotation of pre-Judeo-Christian-Islamic. Surely you’ve noticed that, even if you consider it ill usage.
I couldn’t say either way whether the mystical threes in Platonic philosophy influenced the Trinity of Christianity. If they did, it would be only in a vague and I direct way. As in, some larger Mediterranean idea motivated both Plato and the later Christians, like how a flood motif can be found both in the Bible and Gilgamesh. I’d be careful here, too. Because I happen to know some of the early Christian philosophers were Platonists, in a manner of speaking, prior to conversion. St. Augustine was a disciple of Plotinus, who in turn was a Platonist.
There are other similarities between Platonic philosophy and Christianity, though they’re all very imprecise. He came close, as I waif, to draping the Good in the clothes of divinity. The Doctrine of the Forms has the same sort of lesser reality way Christians look at created reality. Not that Christian reality isn’t real, but Jesus’ kingdom not of this earth is more real, if that’s the way to put it, than this earth. Tge metaphor of light is big both in Plato and the Bible, and with similar import. I believe he posits an afterlife. He definity conceives of a soul. Learning things, for instance, is like remembering them from before you were incarnate. Which sounds maybe like Hinduism, but it’s the idea of something uniquely you transcending matter which I’m thinking of.