Any sentient species that can generate, store, and then convert the amount of energy to either move a sunshade or move the infrastructure needed to construct and then deploy a sunshade at the distances needed to reach inhabitable worlds no longer cares about planets.

They can use that same technology to create, on a whim, inhabitable structures of arbitrary size and composition around any star- converting gas giants (or gas clouds or the solar winds) into perfectly positioned and constructed habitats in ideal locations.

Competition over planets would probably be as foreign and incomprehensible to them as what occurred in the universe prior to the Planck epoch is currently to us.