Is the trinitarian Godhead a person or personal, or more like a divine substance, or...?

Is the trinitarian Godhead a person or personal, or more like an impersonal divine substance that connects the three persons of the trinity by being their common basis? Or maybe both personal and a substance somehow (but how would that be the case)? Or something else entirely?

I'm asking because thinking of there being a divine substance that connects the three persons of the trinity is a new way of talking about the trinity that I just heard about and I find it helpful in some ways. But I don't know how to think about it this way and also think about it (Him) as a person at the same time yet. Maybe someone can help me. (Side question: what even is a person? It's a tricky one to define for me....)

Also, if the trinitarian Godhead is a person with three persons sort of within Him or coming out of Him somehow... how does that work? Are they parts as in different parts of a greater personality? Or is there some better way to think about it?