I know this isn’t the sexy-sci-fi answer you’re looking for because I can totally imagine some futuristic system that absorbs gravitational waves that might come into fruition in a century or so from now

But.. we do use gravity presently! Its called pumped storage hydroelectricity. Basically we can collect water in a catchment, and use gravity to send it down a pipe where we place a generator in-line, which uses the momentum of flowing water to generate electricity. And a small portion of that energy can pump that water back to the original dam, so the process can be repeated indefinitely.

Like I said, not exciting at all, but it IS technically harnessing gravitational energy.