What is the Trinity?

My question for this fellow YouTuber would be, if these three 'Persons" are "within" the one being who is God, is "God" a separate entity altogether? It would seem so given that they are 'within' this one 'being.' It almost seems like there's 4 entities here namely, the Father, Son, and Holy Spirt.. and oh, there's also the "being" who is God!

A follow up question: Since none of these "Persons" in and of themselves compose this one "being who is God", how can each "Person" be "God" since they would have make up the "being" in and of themselves to be "God" according to this definition?

Syllogism:

God = 3 Persons together as 1 "being" in Trinitarianism
God is not a "Person"
Therefore, none of the 3 "Persons" can be "God" in and of themselves, even by Trinitarian standards