Seems like a low risk approach for taking over a planet would be to just park a large shade between the planet and it's star then let it enter a deep freeze. Then you could just remove the shade and let the planet warm back up before settling down.
I wonder how that would look from a feasibility perspective... Let's see - Earth's radius is 6,378 km. Area exposed to the sun therefore would be 6,378 * 6,378 * 3.14 = 127,731,695 [1] If you wanted to block just 1% of the light, that would take a shade of 1 million square kilometers, which would be equivalent to a shade that is 1,130 km on a side. Seems like it would be tough to do given all the dust and rocks float…
Edit: Seems I misread the Starship capacity. This is probably only to LEO. Its hard to estimate but going by the geostationary payload, it would be one third of that, so triple the amount of flights. At a cadence of 2 launches per week it would take 4.5 years to launch all of it. ( 450 launches / 2 launches per week / 50 weeks a year)