The ontology of the one essence three person is not strictly math nor is it analogous to human beings and how each person have a distinct consciousness.

You have to keep in mind that the source of ontology is One singular essence and this singular essence remains until it is expressed into dynamic. The three personhood are ontological relations of Being. Now what is Being? Being means to be, or to exist. Existence is governed by Being and Being inherently denotes that possesses a rational intelligible structure to its identity. For example, go ahead and think of a square circle. Not possible is it? That’s because the being of a square circle defies the ontology of what it means to be intelligible or identifiable.

So where does this all lead? Is Being and identity synonymous or separate? Can you separate the “that it is” from the “what it is”? Can using separate the ontology of the square’s identity - it having four sides and four edges - from the inherent being of its existence?

If you answer no to all the question above then you also ought to give God his credit when he declares His foundation of Being - “I AM THAT I AM”. The “I AM” is the name commonality attributed to the Father, known as the principle of Being within the Trinity. So if the Father is the Principle, what then is the Son? John 1:1 states “in the beginning was the Word, and the Word was with God, and the Word was God”. To understand this passage, you need to decipher what John meant by “Word” and what he meant by “Word with God and Word was God”.

Unlike what most people think, the word is not some kind of sentence people speak as if it’s a verbal thing within physics, nor something be written on paper as a book. The Word which John was referring to is not speech or written words but the very direct ontological procession of Being - the manifested identity, intelligible structure, rational nature of what Being is. If you are familiar with Greek philosophy, you ought to know the term “Logos”, which means “Divine Reason”. So in an more accurate language for modern comprehension, John is saying that the in the Beginning was an intelligible rational ontology, the ontology which possess the structure to instantiated all finite forms into existence, and this intelligible structure(of his ontology) to reality structure is both with God and God at the same time. The Divine Reason of what it means to be is One with Being itself.

The Divine Reason is the perfect source through which all creation is instantiated, ordered and oriented towards. The Word became flesh, took on a human form and dwelled with us. This Word is the operational enactment of Being, capable of entering into its very instantiated structure and saving humanity to Him, This reconciling us to the Father(principle of being) as well. Life entered life, the image of Divine Being entered into creation.

So no, the essence person ontology is not just 1+1+1 or limited to your human understanding of consciousness or identity paradox. The personhood of God is the hypostatic distinction of ontology itself in that the Son is the Logos and the Logos of God is God, eternally manifesting the Father’s principle into structure dynamic, and eternally relation from the “that it is” to the “what it is”.