There's a massive difference between a WWII ship needing the food from a small farming village and a space opera starship needing food from a small farming village.

People think ecology is magic. Like, in the sense that you can't just produce endless food like you can produce, I dunno, endless amounts of steel or something. But it just comes down to energy. Farms take up land because that's the cheapest way to get sunlight on them, and sunlight is cheap. But if you can generate the power to fly up into orbit seemingly as easily as pulling out of your driveway (and remember Kai's little ship could do it too), then you have access to levels of energy far beyond what we can do here and now. It's not reasonable to compare that to what a WWII ship can harness. The WWII ship might as well be a sailboat in comparison.

To have a galaxy-spanning civilization, you almost certainly will need "industrialized" food production. Like, massive hydroponic plants, and many per world. That takes ungodly amounts of energy, but if you can dance casually around gravity wells like they show, then you have that power.

It's not like "galactic empire needs wheat" can't make sense. It's that the movie didn't even make the attempt, and what worldbuilding logic we do see seems to make it hard to digest (no pun intended). It was presented in a taken-for-granted sort of way. Like they hit on that initial conflict and stopped thinking about it or what it would mean for their universe. If it was just that, some nagging issue about food logic at the start of an otherwise tight and satisfying story, I doubt as many would be complaining. But the entire script was low effort and superficial.