

Sci-fi is delightfully circumspect on how an intergalactic empire would work. Maybe Herbert’s Dune universe is clearest and he just took us back to the middle ages with sandworms and drugs, fiefdoms and nobility.
I think whatever area shares the same government is a country. It doesn’t have to be contiguous or on the same body floating through space. It could be the size of the Vatican or half the universe.
I suspect the definition of the word will change once (if) we make it to the stars. We have gone from nomadic life to loosely defined borders to kingdoms to empires to multinational and intranational federations of sort. These terms may no longer be fit for purpose when we colonize Mars etc. And maybe that’s why you struggle to comprehend how it would all work behind the scenes. We don’t know for sure, sci-fi authors don’t know (or don’t want to be too specific and limit themselves in what stories they could tell in the future).
This is the “how much is a pint of milk?” politicians gotcha question of the so-called-AI age.