If capturing CO2 would be done at large scale, obviously it would be done using solar energy, like the plants, or wind energy.

So solar or wind energy is a prerequisite for CO2 capture, followed by the separation from air by physical or chemical means, followed by the reduction to hydrocarbons, either by direct electrolysis or by using hydrogen obtained by water electrolysis.

If I'm reading the literature correctly, there are plenty of industrial processes producing streams of CO2, such as concrete manufacturer, that wouldn't even require separating the CO2 from "raw" air per se. At least the initial success of any electrolysis will probably be as a bolt on to these processes, to reduce their CO2 output IMHO.