This idea of extracting water from air keeps coming back, but every time someone tries it, they learn of the same thermodynamic limits. It is extremely energy-intensive to extract water from the air, and it only really works if the climate is humid enough that there is water in the air to extract. This is exactly what a dehumidifier does, and the off-the-shelf version you can buy at home depot is no more than 5-10x worse than the thermodynamic limits - those generate a pitiful amount of water for a lot of energy intake.
Do we even need to extract the water? The point is to capture weight, and the only reason to liquefy the water is to store it more efficiently, by volume.
Storing higher humidity air doesn't sound very efficient, storing liquefied humid air sounds like a disaster waiting to happen, and storing compressed air sounds like an unnecessarily complicated alternative to just compressing the hydrogen.
You're both missing the forest for the trees, when the airship is electric obviously you don't have to add ballast while flying because you don't have to compensate for burnt fuel.
Not necessarily - the great thing about airships is that they can go anywhere, and pick up cargo at places that aren't ports. You can go pick up logs from logging camps directly, for example.
That seems like it would be really bad for energy efficiency: now you need batteries large enough for propulsion during the whole trip, plus extra for extracting water vapor.
Why not just take on some liquid water at the destination when you drop the cargo?
Because that's less flexible and there may not be water at the destination in the first place. That said, Flying Whales are trying to do exactly that, because ballast tech just isn't capable enough yet.