Perhaps type 1 for the same reason you said. Celestia can control the sun, therefore they should have the ability to harness all of its energy. But the thing is that they don't seem necessarily capable of storing the energy. Plus they also don't really use all of it necessarily, considering their technology doesn't really require much energy to power it.
We're technically around a type .73 civilization, as we can use and store approximately 73% of our Sun's energy, and we should reach type 1 status very soon (article says 100-200 years, though I think it may be sooner rather than later considering how fast our technology has advanced).