Nobody mentioned Scum and Villainy yet? Well then. Check out Scum and Villainy - it's really, really good!
It's an adaptation of the Blades in the Dark system, geared to tell the story of a rag tag of adventures and scoundrel, but in space! It covers politics, exploration, an (optional) Not-The-Force mystic ability, and can be used to run different vibes of games - main inspirations being star wars (obviously), cowboy bebop, firefly, that netflix show about space bounty hunters...all the usual suspects.

The ship is actually sort of an extra character in the party, and can really be the common thread between different campaigns and adventuring troupes - think of the Millenium Falcon. (If you are familiar with blades in the dark, the ship takes the place of the hideout / your criminal organisation).

The game expects an improvising / reactive GMing style more like Torchbearer/Mouseguard or any Powered by the Apocalypse game rather than the classic d&d "GM prepares an adventure" style, but it's actually not an hard requirement.

Also +1 for Stars without number - even if you don't end up using the system, the GMing tools in the "running a sandbox" chapter are fantastic.