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But you can't do this to earth's sun without causing catastrophic changes on earth, so you have to reach a different star before doing this. Blocking out even like 1% of the sun's energy from reaching earth would likely wreak havoc on the earth
No, there's ways to do this without damaging Earth. You could arrange the sphere so that there's a gap that allows light through specifically to keep Earth lit, or you could use mirrors or straight up artificial light sources to maintain Earth's sunlight levels.
Or you get over the obsession with maintaining Earth exactly as it always was and carry on without it. Once we're talking about Dyson spheres a planet like Earth would be a very minor population center. Probably more valuable as a source of additional building material than as a place to live in its own right.
Well, given that the earth only utilizes about 1 billionth of the sun's energy, so I think we could have both with just a little effort.
We'll just keep a window open on that side of the Dyson sphere.