Steel has between 2% and 0.05% carbon, that's not really a lot, particularly when you consider martian colonists will want materials like sugar and polyester that have a much higher carbon content. [1]
There are numerous ways to fix carbon from CO2. If you can grow plants you can make a char out of them which what people used to use to reduce iron and add carbon as an alloying elements. There is a huge amount of research on turning CO2 into CO so that it can be mixed with H2 (then they call it syngas) and then build up larger molecules such as methane, methanol, gasoline, fats, etc.
https://news.mit.edu/2024/engineers-find-new-way-convert-car...
It's not a question of being able to do it but instead doing it better, cheaper, harder, faster, ...
The funny thing about reduction of iron (and many metals) is that it can be done with either of the two ingredients of syngas, CO [2] or H2 and either way you get the oxide CO2 or H2O as a byproduct. If space colonists think that volatiles are precious they'll practice chemical cycling, turning those back into reactive CO or H. On the moon or asteroids I'm pretty sure people would think either C or H2 is precious and wouldn't waste it, I am not sure about Martians (e.g. if you can get CO2 out of the atmosphere it might not seem like a crime to vent it)
[1] people think "technology" and they think "metals" but actually a lot of what you want is made of carbon, hydrogen, oxygen and nitrogen (CHON)
[2] what a blast furnace uses
Yes, the problem is likely not in getting enough carbon (though a kiloton of steel would require several tons of it), but rather having a mass production process advanced enough to precisely control it. Almost all heavy equipment would have to be bootstrapped on Mars, mostly from the inevitably subpar local materials, and ith access to energy that's worse than on Earth: no fossil fuels, no hydro-energy, much less sunlight.
Everyone who's seriously considered space colonization has come to the same conclusion that Eric Drexler did -- you need to have some kind of system that can make absolutely everything with as small a population supporting it as possible.
You've got the problem that there's nothing that could manufactured on Mars that would be worth bringing back to Earth. If a Martian colony was dependent on Earth for anything it would expect to get its resources cut off at any time, and even if you can get spare parts and stuff from Earth the turn-around time counting the synodic period and transit time will always be several years. See
https://en.wikipedia.org/wiki/The_Martian_Way
I think it could be possible with some combination of synthetic biology, fermentation, flow chemistry, 3-d printing and such. It's a good northstar for research into "advanced manufacturing" which could come in handy here on Earth.
Honestly I think one of the possible premier uses of orbital (though not Martian) resources would actually be agriculture. Limiting biological contamination and maintaining sterile environments, unlike other industries, can produce a value-added product compared to the inputs.
Also there's at least a plausible mass trade off - a space borne habitat structure doesn't need to support its own weight against gravity, so you might be able to trade favorably on the launch costs (e.g. grow crops in a big inflatable dome under hydroponic conditions). Certainly it would make enforcing quarantine easier.
Large structures and LEO do look like the closest you could come to the LEO dream. The atmosphere for a baby Bernal sphere that has a usable area of 35 acres would take about 15 starships to send up which would be like getting 1 starship load to the moon. Building something like that which is a simulation environment for Mars might be cheaper than going to Mars.
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