What I don't understand, though: surely they can not be so incompetent as to having forgotten that they need fuel? If all success hinged on the airport, then there should have been some plan B in case of losing the airport?
It's not necessarily anyone forgot they need fuel. It's more likely every readiness report filed in the past several years has said "everything is awesome". The reality being that nothing is awesome and actual readiness is a small fraction of what the paperwork says.
So the general staff assume everything is awesome and they've got plenty of supplies and logistical ability. Now the disparity between the state of their forces on paper and reality become known. Even if the military planners assumed reported status was exaggerated by some amount, the reality is likely worse than that assumption.
Keep in mind the Russians have been building their forces up on Ukraine's borders for months now, in winter. Even if everything was great that's a lot of food and fuel needed just for soldiers to sit around and more to actually conduct exercises. Then after months of burning through stocks of food and fuel they go on the offensive which takes even more food and fuel.
I only have experience through EU4, and Civilization; so take this with lots of salt. But look at the map: Putin is avoiding some cities (Sumy, Okhtyrka, Chernihiv from the East) to get to Ukraine. He is not taking cities and moving forward, he's avoiding them to get to Kiev quickly. This is suicide. If his Kiev plan fails, a major part of his army will be trapped with bad logistics.
Putin is desperate. A quite perilous situation for a man with lots of nuclear nukes.
Cities are really hard to capture and hold, with a defender advantage of 1:5(or up to 1:10 of defenders to aggressors. depending on who you believe) napkin maths suggests that a quick city siege is 4 months.
So that blows your time budget out of the water. Kiev is reasonably close to resupply (assuming the logistics is managed properly.....)
Its far wiser to avoid the cities with a bargepole.
