Its pretty simple.

Hydrocarbons + oxygen + ignition releases energy, H20, and CO2.

Energy + CO2 + H20 can synthesize hydrocarbons.

There is plenty of interesting research how to do the latter - but it doesnt change the fact it just reverses a process we currently do by the tanker ship full. Why would anyone do that at scale?

It cant have a large scale application until we basically have free energy from some other source - and at that point, synthetic fuel is probably still a terrible way to store and use energy for pretty much everything except jet airplanes.