What Aristotle has to say is irrelevant.
You cannot understand the meaning of "substance " or “essence” or “nature” without having some familiarity with Aristotle. Much of the discussion here revolves around these terms.
The meaning of “person”, as distinct from “substance”, is also relevant.
“Substance” responds to a “what” question; “person”, to a “who” question. “What” and “who” reflect two different dimensions of reality which are not interchangeable.
I agree that the notion of the Trinity is tricky. Divine Substance is only “first” substance; there is no “second” substance. A “first substance” is the concrete entity, e.g., this tree in front of my house. A “second substance” is the nature or essence of “this tree”, a nature that defines other trees as well - this is “second substance”…For more on this distinction between "first and “second” substance, see Aristotle’s metaphysics.
And, again, the meaning of “substance” in Aristotle cannot be applied univocally to God.
That is, there are important differences between Aristotle and Christian theology.
First, the “whatness” of God is only “first substance”; there is no “second substance”, i.e., a nature that can be shared with other entities.
Second, God’s “substance” cannot be defined by genus and a specific difference.
Third, in God, there is no real distinction between “essence” and “existence”.
Consequently, God is not just one entity among other entities, not even a Supreme Entity.
Aristotle’s God is one entity among others, and is a Supreme Entity. Aristotle’s God is part of the inventory of the contents of the Universe. The Christian God is not. The Christian God is “outside” the entire Universe (i.e., is not a part of the cosmos).
Therefore, we have to use a type of analogy when speaking of God.
Analogy is not a dishonest maneuver
It’s just that meaning is not always univocal. And this absence of univocality allows us to say, without logical contradiction, that there are three Persons and one “first substance”.
We cannot talk this way about beings within the Universe. For example, there is just one person paired with a human being, a “first substance” of “rational animal”, However, that “one person” is not just a"rational animal" - Abraham Lincoln has more ontological density than “rational animal” (otherwise, to say Abraham Lincoln is a rational animal, and Thomas Jefferson is a rational animal, would be to assert that Abraham Lincoln is identifical to Thomas Jefferson).
Another way of saying this: there is no genus and specific difference that defines Abraham Lincoln qua Abraham Lincoln, i.e. qua the “person” of Abraham Lincoln; however, there is a genus and specific difference that defines Abraham Lincoln qua human being, i.e., “rational animal”.
Abraham Lincoln and Thomas Jefferson can share the same nature (“rational animal”) but at the same time be two different persons.