The bottom line is that no matter what the zero-point energy is, it’s the background of the universe on top of which all of physics takes place. Just as you can’t go lower than the ground floor of a building with no basement, you can’t get lower than the ground state of the universe — so there’s nothing for you to extract, and there’s no way to leverage that into useful applications of energy.

So, unfortunately, any work you do in the universe will have to be done the old-fashioned way.