For context: I'm writing a story where the main antagonist is an empire that builds Dyson swarms around every star they can get their hands on. The protagonist lives on a planet around one such star, and over the course of several years, he watches as the planet's climate changes from one resembling Earth today, to one resembling Earth during the last Ice Age. If the Dyson swarm is completed, his home planet will be rendered utterly uninhabitable, and the protagonist's desire to keep that from happening that is what motivates him throughout the story.
I've heard that blocking roughly 2% of the sun's light would be enough to lower Earth's temperature from where it is now to pre-industrial levels. So what percentage would you need to block to lower the temperature to uninhabitably cold levels?
Also, some related questions: could a Dyson swarm block out enough light to do this, or are Dyson spheres needed? At what point does the dimming of the sun become noticeable to naked eyes on the ground? How would the cooling be affected if only one side of the sun was being partially blocked?