Does the energy of the soul get replenished by energy arising from the zero-point field?

This is not the case. This is energy from another dimension where the higher astral plane resides, so it is an interdimensional transfer taking place to allow human beings, as a physical extension of the soul, to be present in the physical plane of existence yet still connected, and now you are seeing the reason for the terminology, "interdimensional DNA," because that speaks directly and purposefully in describing that it is a bridge between dimensions for conveying the life force energy that animates physical beings on all levels—physically, mentally, and intuitively.