Okay, first off, I have at best glanced through the rules so far for ships in Starfinder, but is there anything preventing a bipedal form for your ship?
There are no hard rules governing the appearance of your ship whatsoever. That said there are also no rules on how to handle anthropomorphizing your ship either.
So you can say it looks however you and your GM can agree on. But there are no official mecha rules yet.
Seeing as they just announced a gear and vehicle book for next march? I would say there may be then. Or you can do a google search for any of the homemade Mecha systems on the web.
I made one.
I don't know about a ship in a human-like form; it seems woefully inefficient. But personal "fighting vehicles" is another matter. I can see them as ground combat weapon systems (though, again, there are usually more efficient ways to do that job).
Billantrix (the Silver Dragon) finds the whole idea rather silly. She'll hire a mecha pilot for a specific job, but usually finds the idea of a tank or fighter in humanoid form in poor taste. If you want to impress her with your sense of cool, you might want to build one in the "far superior" shape of a dragon....
Technically, the flight frame Power Armour would be just as capable of space flight as most other Flight options, albiet we're talking on a different scale and map than space ship battles normally use, so... Gundam style space battles with Flight frames are possible.
... The problem is its not going to be as powerful as a later level Power Armour, so it doesn't scale well.
There's a couple of ways around this, but it depends on the GM. They may allow you to fly with a Jetpack/Forcepack on your light Armour while in the Power armour (given you can wear a Light Armour in a Power Armour); or if you're a Technomancer, you could just make your flight spell the spell you maintain with your spell Cache.
If your GM doesn't like the idea your Light armour can do stuff while you're using Power armour, and you're not a Technomancer... You could just decide to use other kinds of upgrades to the Flight frame that might be more useful (like temporary hit points) and spend the rest of your credits on personal Upgrades and other augmentations.
... Or... Just get someone else to cast a Flight spell on you, or use a Spell Gem to do so. Or really, a Spell chip in a computer, knowing that it might work easier.
I'm expecting an archetype or two, maybe a few more options for the base classes.
Given what was found at Azlant Ridge, I suspect the Azlant Empire have some anthromophic power armor.
Mechs via Starfinder
Competition:
https://www.youtube.com/watch?v=8K8lwn5lJAE
https://www.youtube.com/watch?v=RTDg08gMV2Q
https://www.youtube.com/watch?v=DlhtVgB7QuY
https://www.youtube.com/watch?v=TU0MmjraKbo
85% Survival rating
Competitions is the training wheels for Mechs. Hard enough hitting to cause pilot death, but normally a high survival. Competitions range from demolition derby, combat racing, and 1v1 combat. Big money, corruption, sabotage, corporate warfare (legally).
Ground Warfare:
https://www.youtube.com/watch?v=h_PKgztP0zw
https://www.youtube.com/watch?v=vZWxgLQZano
https://www.youtube.com/watch?v=YK38WzlNvfk
https://www.youtube.com/watch?v=15mfslsD_Bw
50% Survival rating
Warfare is the mainstay of Mechs. Ground pounder wars makes sure you have a place to go home too, even if it is just a base. Mechs are treated more a combination of infantry, tanks, and artillery. Mech designs varies depending on race, culture, and role type. Some might be light for scouting, others heavier for heavier calibur guns or multiple missile racks.
Space Warfare:
https://www.youtube.com/watch?v=CoplnxPv-J0
https://www.youtube.com/watch?v=F4Wl0p_TF0Q
https://www.youtube.com/watch?v=TIcYvE231q8
https://www.youtube.com/watch?v=mYe_-oFkMaI
32% Survival rating
Mechs for Space warfare are the infantry. They are deployed in the same manner as starfighters and bombers. But with the capability to capture ships or asteroids or planetoids. Ace pilots have the ability to master the momentum of their mechs with their knowledge of momentum in space. Space warfare is the most extreme for pilots, without the safety of a EVAC suit or being planetside, pilot losses sky rocket for any space domination campaigns.
Agriculture/Construction/Mining/Forestry:
http://www.sarna.net/wiki/AgroMech
http://www.sarna.net/wiki/AgroMech_Mk_II
http://www.sarna.net/wiki/Harvester_Ant
http://www.sarna.net/wiki/Ranchhand
Non-combative 99%/Combative 50% Survival rating
When your back 40 needs to be done in 10 minutes, clear cut a acre of forest in 15, an extremely dense vein of ores, or build a city instantly, civilian mechs are helpful. Each can be categorize in four categories; agriculture, construction, forestry, and mining. Those classifications are self explanitory. Agro mechs can be crop harvesters or herders for large herds or herds of large farm animals. Construction can build entire cities from the ground up. Mining mechs can extract materials in larger quantities than an whole team of miners in more dangerous areas. And Forestry mechs can clear large swaths of land. When push comes to shove, or even resistance groups needs mechs now. Each can be retro fitted with ranged weapons, leaving their initial farm tools as melee weapons. Having civilian mechs in your force can make training easier for resistance mech pilots who are not familiar with mechs designed for war.
At the bottom of the post text box below the community guidelines is a spoiler box that lists how to link sites.
It is bracket the letters "url=insert.address.here.com" close bracket. Then type what you want for the link text and finish with another bracket "/url" and a closed bracket.
Didn't have time to go through to code everything right. Was using my phone.