The Moon and the Earth do act as one mass if you zoom out enough but every person has their own minuscule gravitational force as well. Even the ISS is attracting the earth toward it. Beyond that, that massive rope you’re using will have its own gravitational force that, if not created from resources on the moon or earth would introduce its own gravitational forces. As far as the energy you’d gain fro. The moon moving away from us, yes theoretically, you could harvest energy from it. At that point however, you’d already have build. System that re-orients the rope to the moons position relative to earth and if you have a track/system set up to accomplish that Herculean task (think The Line x a billion) you could just use that orbital motion to create as much energy as you need. It would be cheaper and probably more efficient to just build structures that harvest the current tidal energy the moon produces in the oceans. Hell, I’m sure you could build some giant canal and put a hydro-electric damn in the middle that creates power both ways. That would solve for your rising oceans problem a bit too. Alas, even these tiny versions of ideas are still multi-trillion dollar projects that no country, if not the entire worlds economy, could afford.