Cyberpunk

Space Sweepers isn't like a western at all. Everything is dirty and broken and the space ports are more like cyberpunk cities while Firefly would visit frontier planets. There is a bit of a "found family" trope in both Space Sweepers and Firefly but that doesn't have anything to do with whether they're cyberpunk or not.

Just watched it (and am very glad to have seen this recommendation -- the movie's rad as hell!).

I'd say the big difference is in the aesthetics. A lot of core cyberpunk themes have kind of pervaded mainstream science fiction at this point, wealth disparity, classism, evil megacorporations etc are common, even in stuff I wouldn't say makes the cut. Sort of a genre dilution.

There's a hint of it in Firefly but they leaned really really hard into the 'western' part of the space western, especially in the aesthetics. Everything from the clothing, weapons, dialects, the planetary frontier sets, even the warm yellow lighting they use most of the time (contrast with the colder, more blue color pallet from the movie which was a bit more cyberpunk, I think to its detriment).

Thematically, Firefly lifted a bunch of plots like train heists straight out of westerns, and the whole backstory around the civil war and the overreaching government as the bad guys was playing with elements from confederate apologencia in older westerns.

Aesthetically Space Sweepers sweats cyberpunk out of it's very pores. The ships, the habitats, it just looks awesome, and I feel like you could trace some of the clunky tech all the way back to Alien. There's a similarity between the two in that they're both about dysfunction crews on a ship they're too poor to keep running (Cowboy Bebop also says hi) brought together by the person they're keeping secret/protecting, but it's what they do with it.

And it has some core cyberpunk stuff in it: wealth disparity and a megacorporation owning the only livable biosphere, the corruption and inequality, the orbital habitats as megacities, basic services being turned into for-profit enterprises. It's literally high-tech low-life, (one of the lowlifes is high tech, she's a military robot). It's a little cartoonish at points (especially the bad guy) but the adventure tone actually carries that well, even if it's a little further from the morally ambiguous tech-noir type stuff you would see in something William Gibson wrote.