Plants get there carbon out of the air and release it back into the air in equal quantity, that's what 'carbon neutral' means... you can effectively sequester the stuff merely by increasing the amount of biomass on the planet, not just by dumping it back down in holes, which we can also do but in my opinion is needlessly wasting a valuable resource... I'd rather just see the biomass per acre increased in various spots like desert or tundra... but you miss a key point, one can sequester carbon by growing biofuels and simply storing them in cisterns as economic reserves. I'd rather have megatons of biofuel in a bunch of cistern then just dump carbon back into empty mines.

I don't think space-based agriculture for terrestrial consumption is likely to be economically viable under any realistic circumstances, even if we never had anything better than solar and had to use space tethers to transport food it is cheaper to move raw electricity and heat... you'd dump power from orbital solar plants down a tether to massive many story hydroponic facilities and purge waste heat right back up those tethers or five mile high heat conducting towers. Theoretically you could pack trillions of people into that sort of setup essentially limited by how much heat you could pump out, and you'd probably be looking at something along the lines of a 100 kilowatts per person, though you could probably dump that down a good deal by only generating in hydroponic facilities the exact right amount of the proper light spectrum for optimal. That heat could only be ultimately radiated away... which is about 500 W/m2 at room temp but presumably one could construct the big orbital solar panels to have a surface area larger than their effective collection cross section of ~ 1300 W/m2 IIRC at this distance from the sun, nice crinkly rear sides, a straight flat panel would doing 1000 W/m2 while absorbing 1300 w/m2 which is no good but one with a pin backside like the heat sink on a processor usually has about 50x the exposed surface area of it's flat equivalent so presumably doing 25,000 W/m2 wouldn't be a problem, but I'm thinking the upper end of conductive heat transfer is around 5000 W/mK... which does happen to come from those same kickass new materials constructed out of carbon that one would tend to build space elevators and many-mile arcologies out of so I'd bet on being able to push out the heat loss to an order of magnitude or more above Earth's own current stabilized hundred petawatt or so amount... so maybe 10 Trillion people? If they all pretty much lived and grew food in ten thousand story buildings you could pretty much use 2% of the Earth's land surface for that with plenty of room for food crops and individual apartments larger than most mansions... pretty far into future to be sure but physically doable by known laws.