The Kardashev scale is most likely a misconception anyway: the factor representing capability is power density, not total energy. It is useless to generate hug

The Kardashev scale is most likely a misconception anyway: the factor representing capability is power density, not total energy. It is useless to generate huge amounts of power thinly dispersed over galactic scales. A society capable of high power densities, like direct energy-conversion fusion for starters, can realize fantastic feats, as opposed to somebody collecting sunlight over vast volumes of space, but lacking adequate portable storage.