In this particular case, they are planning to take energy from carrier's nuclear power plant. More generally, either hydrogen or fuel synthesis requires energy

In this particular case, they are planning to take energy from carrier's nuclear power plant. More generally, either hydrogen or fuel synthesis requires energy to come from somewhere; In this regard it is no different than re-building airplanes to use hydrogen, as the original article suggests. The point is that we might have better chances synthesising fuels usable in existing planes, versus re-building majority of aviation to use hydrogen.