God simply has three persons. I would argue the objective reality is that there is a Father, Son, and Holy Spirit, as revealed by Scripture and Sacred Tradition, and thus “3 persons” is simply a description of this reality.
Considering that the term “Trinity” is not in scripture, I suppose that the exact number of persons, in and of itself, is irrelevant to God nature. Jesus spoke only of the role that the Father, Himself, and the Holy Spirit played, but did not emphasize for instance that these persons were a “recipe” for God’s nature.
The early ecumenical councils did verify the objective truth that there is a Father, Son, and Holy Spirit, and ONLY a Father, Son, and Holy Spirit constitute God. But the number of persons is, I suppose, a mere accident (in the philosophical sense) of God Nature.
The number is important only when distinguishing the truth from heresy. Unitarians, for instance, believe in roughly only the Father as the true God. Jesus was creation, albeit a begotten creation with a divine and human nature, and the Holy Spirit was simply the soul of God the Father. The fact that there is only one divine person in God in Unitarianism is irrelevant; the heresy is denying the divine personhoods of God the Father, God the Son, and God the Holy Spirit.
So I think numbers are just a human construct to describe an objective reality. I think God is simply the Father, Son, and Holy Spirit, and its simply convenient to call this objective truth a “Trinity”. The “Dogma of the Holy Trinity” is then simply using the weight of Sacred Tradition when teaching this objective truth about the nature of God.
Simple enough for you?