We already have it, it’s called electrically synthesized methane/propane.

If the carbon is captured from the atmosphere and merged with water via renewable sources, that is it. We don’t do it and it isn’t proposed because the efficiency losses are crazy, and we aren’t in a world with over-abundant renewable energy widely available for pennies on the dollar (yet)

Yeah, with the addition that if you're going to go the synthetic hydrocarbon route you might as well go all the way to a fuel which is a liquid at normal operating temperatures to simplify logistics (and which isn't a massive GHG when it accidentally leaks like methane).

Advantage of shorter carbohydrates (like propane) is that they're made up of less carbon relative to the hydrogen (compared to longer chains), so for the same amount of energy stored, you need to capture less CO2 from the atmosphere or from wherever you're taking it.

Propane can relatively easily be compressed to be liquefied at room temperature. Takes just a few bars of pressure.

Let us quantify your statement!

By my calculation, you need to capture 0.9176 carbon atoms from the air to make propane whose energy content is the same as octane made from 1.0000 captured carbon atoms.

I used the "Std enthalpy of combustion (ΔcH⦵298)" of the 2 fuels from Wikipedia in my calculation.

... which of course requires hydrogen.

Biofuels are one way. Basically get algae to absorb CO2 and produce fuel.

Especially interesting because you can just mechanically press the oil out, which is very easy to turn into diesel. Unfortunately the cost/benefit doesn't seem to be there yet.