Why would an alien civilisation go to all the trouble of encasing a star when they could just create Fusion which is the power of a sun.
I can think of 5 reasons off the top of my head.
1) It's the same type of process, but the scale is so different that it's effectively a different thing. The sun has an output in the region of 100,000,000,000,000,000 very high capacity power stations(*). The sun is not a particularly energetic star. There would be a practical limit to building power stations on any planet. You just couldn't fit a hundred million billion power stations on a planet.
2) There may be other limiting factors in building practical fusion power stations. Resources, waste. There will be some, probably including some radioactive waste. Not much, but a hundred million billion times not much could add up to a lot.
3) Living space. Part of the point of encasing a star is to create a habitable area far larger than the surface of a planet. A sphere around the sun at the same distance as Earth would have a surface area well over 500 million times the surface area of Earth. Enough for trillions of people to have acres of land each and still have planet-sized uninhabited nature reserves.
4) To do it. An advanced civilisation might well want a huge, difficult and inspiring project.
5) To enclose themselves. A civilisation might turn inward for various reasons.
* Not a joke or hyperbole. Estimated total output of the sun is in the region of 4x10^26W. 4x10^9W (4GW) would be a very high output for a power station. There aren't many that can output that much energy.