Space Sweepers is a fun "cyberpunk in space" movie
This movie is only two years old so maybe everyone here already knows about it, but definitely check it out if you haven't seen it. As far as I know, it's only available on Netflix.
Space played a big role in Frontera, by Lewis Shiner, which would count as Protocyberpunk if not cyberpunk. A desperate corporation in a post-government world scrapes together the last bits and pieces of the space program to send some agents to a struggling colony on Mars because they want something from the Martians. It's pretty gritty in space travel details as far as I remember, and uses that to really drive home that this is a collapsing society surrounded by a deadly void.
Same for Count Zero as for Necromancer - The scenes in the Japan Airlines Terminal and the floating wreck of the Tessier-Ashpool core where Wigan Ludgate lived were all in Earth Orbits.
Cowboy Bebop takes place all over the solar system in a mix of space habitats and planets, but treats it pretty casually.
Hostile Takeover by Susan Shwartz takes place on a space colony I think in the Asteroid belt. Space travel is pretty rough but not as crude as in Frontera, which was aiming for basically realistic. The ships in Hostile Takeover are better but they still freeze the indentured people as cargo because keeping people healthy all the way out is difficult and they devote those resources to the 'important' passengers. Freezing doesn't give great odds of surviving the trip.
Do the Murderbot books count as Cyberpunk? They've got plenty of the elements. All of them after the first involve space travel. In fact, space travel is what allowed the Corporation Rim to form.
Transmetropolitan mentions space travel, their society has it and has even encountered extraterrestrial life, but they don't go to space in the story.
The two Alien movies are often counted as cyberpunk and space plays a big role in their plots, the isolation of their settings, the aesthetic of the sets. I think these and Murderbot are the only examples I can think of that leave our solar system.
I'm not sure if Outland with Sean Connery counts as cyberpunk. Alien and Aliens seem to, and Outland has many of the same awesome visual aesthetics, but it's admittedly light on cyber stuff. A colonial martial assigned to a mining colony discovers a conspiracy using eventually-fatal drugs to drive the workers to be more productive. He pisses off the conspirators and it's basically High Noon in space from there on. Space is a factor in the isolation of the setting and the awesome sets and miniatures.
When Gravity Fails ironically features no space travel.
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.
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.