More specifically about the suits. I'm picturing cyberpunk type stuff but lets be honest, Humans are humans. There's going to be helmets covered in fauxhawks and stickers, someone's going to opt out of everything practical in preference of a prehensile tail, we're going to express ourselves in thousands of ways. But functionality/general aesthetic I'm picturing for Katie, at least, is starting to form in my mind so you're going to get that.
I mentioned a back mounted drone thing and I'll be honest, it's pretty inspired by Stray. One shoulder has a little thing like that, but probably in grey or black to blend in with the average guts of a ship. Maybe the drone itself is clear so that it's even harder for the giants to notice. The other shoulder has a speaker that can pop out that amplifies her voice to communicate if need be. I picture the grappling system to launch from the wrist but the line is actually attached to the waist and the suit works and supports like a rock climbing harness. Backpack is full of all sorts of tools, and Human-Grade adhesives and anchors. Cable management is hella important and superglue and duct tape have evolved to have built in pest repellent.
The Helmet itself is pretty cliche cyberpunk, but it's definitely got gills for aqua or other liquid adventures. There's a mic and earpiece in it of course, often synced to the little drone so she can scout rooms without exposing herself. It's got a little projector as well, mostly used to throw schematics up in place while you work on a problem. (think Ironman).
People have mentioned Magnet boots in the tags and replies, and there's definitely something there. I joked about rollerskates because I LOVE the idea of a little human zooming around underfoot across the smooth floors of a ship. Katie probably has some highly grippy-yet-silent shoes that are closer to those a rock climber would wear; form fitting but not restraining, flexible but still supportive. You need to be able to FEEL your foot placement running across wires and climbing up cables. There's also some ship-rats who insist on running around barefoot. there always have been and there always will be.
I like the idea of the suit having instead of typical oxygen tanks, algae tanks of some kind? like the oxygen is coming from plants that are growing symbiotically from the wearer's waste. They would be small. I Don't like putting too much on the back of this kind of thing because humans need to roll to absorb impact, and even with lower gravity there's a lot of fall risk in this industry. That's one of the reasons as much as possible is on the toolbelt and only bulkier tools would be in the back pack. in emergency you can attach it to the drone and have that hover in a safe spot until you call retrieval. So maybe the plants would be in a living space and the air just circulates through the suit, then you hook up to the plant take to refresh overnight? We know that For sure there's lots of plants and algae tanks in the homes of humans living in space, but Brownies like Katie don't exactly settle well. She's got the wanderlust in her that her parents realized they couldn't conquer, so instead they bought the best gear they could.
That is why short of getting crushed she's not going to be very seriously injured; she could survive in the void for a short period of time in that thing, it's puncture and slash proof, basically anything but blunt force trauma is going to bounce right off. The suit is armor, and it's all about safety. grapples and ziplines and tools are all well and good, but they mean nothing if you get cut in half by a cord snapping or a pissed off space-bug.
Obviously phasers and blasters and all sorts of weapons exist. We love making every kind of science into weapons. Katie relies on what the galactic committee classifies as a "Laser cutter and defabricator" and what humans call "Laser Rifles." She's also got a bunch of tools for cutting through metal that would work on pretty much anything if she needed it too. One of the most important tools, though, would be the spray can- (What did you think i was going to say?) A little can nozzle that can be dipped in anything you use to write, and then sprays it on a surface. Humans communicate through ten foot tall letters out of necessity when talking to Giants, and Graffiti artists figured that shit out forever ago. Katie's model is fancy and can dye the ink different colors if needed. Spray color coding wires and parts is always helpful, especially working in unfamiliar systems.