God dammit they (both him and Democritus) actually thought the stars were small bright objects and they were local to our kosmoi, kind of like a world-sphere that contained the earth, the sun the stars, which was encased within an outer layer of debated constitution. This would also contain the Milky Way, it's local, not something immense in scale that we are part of. Then past our kosmoi there is pan (void) filled with atoms and other kosmoi which could be similar or different to ours. It's kind of like that artwork you see of multiverse theory except each sphere is much much smaller in scale.

https://www.cambridge.org/core/books/abs/greek-cosmologists/cosmos-of-the-atomists/48AFD1C466C35BC79CABF8CB82CF7720#access-block

Quite disappointing overall.