"Advanced manufacturing" is of interest here on Earth for the reasons headlined and for many others (how can a country like Argentina escape the trap it is in?)
Fermentation combined with synthetic biology is an attractive approach but struggles in terms of cost. Anything that comes out of a petrochemical plant costs about 50 cents a pound [1] whereas carbohydrates of plant origin cost about $1 a pound [2]. One of the renewable energy "El Dorado" technologies is ethanol from cellulosic biomass [3] which is straightforward to demo but is nowhere near being cost competitive -- during WWII there was a revolution in fermentation that got the cost of penicillin down by orders of magnitude but cellulase production has been worked on for decades and seems to be near the limit.
[1] https://www.statista.com/statistics/1171072/price-benzene-fo...
[2] https://www.statista.com/statistics/236628/retail-price-of-w...
To the actual question here: As for why we don't use microorganisms (or algae) more for carbon sequestration. I guess packaging and protecting them to keep them alive is very costly. More packaging needed than solar panels due to (~10x?) lower efficiency. Same reason we do most of our farming still outdoors not in expensive but against hail and wind protecting and growth rate boosting hard glass roof greenhouses or even nicely pest compartmentalizing and massively land area saving vertical farming.
Nanofactories (and machines made by them) could make building say algae-panels >99% cheaper eventually. Though as mentioned it will take a long time till we have these devices. Even with dedicated efforts which we currently do not yet have enough of.
In the meantime till we have such amazing technologies we have to look for other solutions that work.
No packaging needed fertilizing the sea with iron I find to be scary geoengineering. Makes me worried about anoxic dead zones if overdone. Messing with the ecosystems we'll likely kill even more species by bringing it out of balance making the algae population deliberately explode.
Classic non-biological methods not messing with the ecosystem like solar panels seem to work well. But storage is needed too. Yes not carbon sequestration here, but for storage green hydrogen seems good if it could be made just a bit more efficient in conversion. Nicely seasonable storeable for the "dunkelflaute" in former natural gas reservoirs. I don't buy that "we can't do that because embrittlememt of gas pipes" argument and the "funding green hydrogen funding natural gas" argument.