I didn’t get anything about society’s stability from the story to be honest, and I find the premise rather abstract, considering humans will never be around to experience a dying Sun (in fact, the Earth will turn into a completely inhospitable Venus-like planet long before the Sun.
Which, again, is not necessarily a problem, but its impact can only be as strong as any other unrealistic completely fictional idea. I brought up The Lord of the Rings not because I think your story has to be that complicated, but because that story is pure fiction and yet gets people fully invested in its world. The fact of the matter is if you want quick and efficient investment into your story, it needs to be grounded. The less realistic your story is, the more work you need to do before it really makes an impact.
I think if a dying Sun is a really interesting idea to you as a sort of fantasy horror concept, you should spend more time really creating a fantasy world that a player can get invested in despite its lack of connection to the real world. Alternatively, create a sci-fi scenario that at least somewhat creates a veneer of realism. As it is, you show a flat Earth – something so obviously at odds with known scientific reality that it’s practically a meme at this point – and a giant room with a giant lightbulb. If you at least made your universe somewhat grounded by saying that humans moved to Mars or something, and if the World Government established some kind of nuclear-powered light-producing satellite or whatever, I might be able to suspend my disbelief enough to take your story seriously with less investment.