Russian soldiers yell from the ditch nearby "Stalker are you gonna use that?"
Stalker laughs and says "no of course, take it just make sure to go back the same precise way I went in and you will be safe!"
On a serious note, this is a concrete example of how serious Russia's logistical issues are do to a logistics vehicle (especially lightly armored transportation vehicles/APCs) shortage.
Do a quick google search for "wars that were lost because a numerically superior army on the offensive overstressed and outran its logistics capability", it might be almost all of them.
Honestly this is a terrible strategy as how can Russia ensure that enroute that the carts don't become traps for the Russias meeting up to resupply from them? Either literally Ukraine could intercept and place explosives on the cart or an intelligence drone just follows the cart until the soldiers come out of the bushes to get their food and water and then the drone calls in an artillery strike.. end of story.. Humans driving a lightly armored logistics vehicle or an unmanned small ground vehicle driving erratically as it moves to an unknown destination would be much harder to predict. Really, in the day in age that FPV fiber optic drones can loiter and wait on the ground next to the tracks, this is the kind of solution you try when all of your good solutions are no longer available for you to choose. Russians are fools to continue this war.
The main defense a rail network has is that it is fairly easy to repair track at an industrial scale so long as you can clear the area and rebuild, and as a result that even though a train is a very very vulnerable large loud target, it is difficult to know WHEN to ambush a train because you might just be standing in the middle of nowhere for hours and the train never comes before hostile patrols make contact with you.
Under this logistics system however rail networks become constant sources of intelligence on enemy movements, this seems like a disastrous idea to me given the sophistication and skill of Ukranian UAV and unmanned ground vehicle operators. Also, it wouldn't take much to stop a whole kilometer long length train of these unmanned logistics carts, you just need to blow the one up in front with an FPV drone and the rest of them are stuck. This is the war equivalent to placing a traffic cone in front of a self driving car in order to immobilze it, and by virtue of not using a truck or a train with a human driving it Russia leaves itself open to massive amounts of logistical disruption this way... which is what loses wars ultimately.
As you point out Russian troops are screwed if they aren't near train tracks but that also means Ukrainian intelligence can assume the Russian troops are having to tactically come within a certain distance of tracks to resupply which makes their movements massively more predictable and easier to disrupt. You just look at a satellite image and start drawing lines to the closest rail lines in enemy territory and extrapolate from there...
Trying to predict where an MRAP or APC will rush in much needed supplies to a heavily suppressed defensive unit on the otherhand is much harder to do both from the increased mobility standpoint but also from the standpoint of needing to muster a far greater degree of precise firepower needed to knock out the logistics vehicle even if you can predict where it will be.