If everyone has nonlocal consciousness, a scientific term for intuition or psychic perception, which extends everywhere at once as one of its properties, there must be a veritable sea of interpenetrating, complex, nonlocal consciousness energies from countless sources. Is that vast body of consciousness a part of the zero-point field or separate from it?

We would say that the pool of nonlocal consciousness generated from sentient beings coexists with the zero-point field. It is in another dimension and this is complicated to describe in human language because multidimensional space is beyond human comprehension. You have no reference point to describe it other than mathematical expressions and those are not easily deciphered to hold a model in one's head, something visual, for example, like a sea of consciousness that might have depth but great complexity with many things going on within it, where things impinge on one another, interact, and transfer energy to make alterations with consequences, and so on. This description we are imparting is, as well, very akin to human experiencing of the physical realm but it is not so totally foreign from other dimensions in the way energy interacts and modulates things. So it is a useful starting point for this discussion. The zero-point field of physics that gives rise to what you perceive of as matter and other forms of basic energy like electromagnetic emanations, has a different configuration than nonlocal consciousness and less in the way of refinement with content. The point of differentiation here is that the zero-point field energy is not yet giving rise to a creation, whereas nonlocal consciousness is itself, by definition, a creation because it has within it the intention of a sentient being, which imbues it with information content having both an intention and a purpose in some way or another. So it is far more than simply raw energy as is present within the zero-point field.