Hmm, obviously cyanobacteria like Spirulina[1] "utilize CO2 captured from air" along with "water and some minerals" and sunlight to make sugars and proteins which people can eat. Not sure I'd describe that as 'fermentation' though if you do anything in a big vat it's a bioreactor and not just... a big vat, apparently.
1: https://en.wikipedia.org/wiki/Spirulina_(dietary_supplement)