And why would energy be the limiting factor? Maybe the limiting factor will be accidental entanglement with the environment of your quantum computer, and you want to cool your system waaay down to avoid thermals interfering with your finely tuned computation engine. Having a hot sphere around a star seems like a terrible set up to do that. Maybe sitting out in a hydrogen cloud and running well controlled fusion would be a much better for that.

I'm not saying one or the other is more or less likely, but the range of possibilities is vast and unimaginable. The idea of energy (in the sense you and I use it now) is not even 400 years old. Harnessing ever larger amounts of stored energy was the hallmark of the industrial revolution. Declaring it to be the fundamental law underlying civilization is like concluding that the earth is flat: You mistake the shape of our immediate environment (the recent past and short term future) for the structure of the overall thing.

We are quite definitely headed in the next couple of hundred years for an end to exponential growth in energy consumption. Exponential growth near where we've been would lead us to cooking the earth in 300-400 years. By the time we're capable of doing solar system scale engineering we will have had millennia of 'culture' that exists within a constant energy envelope. What these entities will value, or want to do is beyond anyone's guess.