For the Arashi, I want to assume not every inch of the desert is sand, sand, sand, rocks, and more sand.
There has to be some kind of water source. From what I can tell, in the map "Canyon Ambush" the large silos have plants growing off of them. Perhaps this is due to condensation, and these towers actually tap underground water supplies. That being said, such places would provide a large, though limited, source of water for a larger population of people. There are also other methods of getting water from cacti, cacti fruits, solar water stills, morning dew, etc. Lore also states that Arashi reuse old factories, either using them for intended design or making them into something else like a shelter, so perhaps they also have dehumidifiers and other pieces of tech. As for food, some websites say most cacti fruits are safe to eat, and it's not like you can't have sheep grazing so long as you stick to the shrubs, and away from the dunes. Another quick search tells me people can herd animals into the deserts for meat and milk, and eating lizards would be common. Bugs are not out if the question either, and I'm sure you have heard of like, scorpions being roasted or other things.
As for like, large banquets of fine cuisine and the such, I'm not sure if the Arashi have many luxuries outside of like roasted lamb, lizard on a stick, etc. I did read that they mentioned rice was something some cultures used. Overall though I don't know enough about Arashi to consider anything outside of flatbread or something. As is I'm struggling to identify how these people really live, because their outfits are very colorful and cultural, well made and nice, while I think the ship design looked like a glued together scrap heap.
As for the Yesha I think it's safe to say a lot of asian dishes, mostly consisting of rice, noodles, vegetables, etc, there's not much they can't make from what I can tell. Their lands have vegetation, lots of space to grow crops, raise animals, and it stretches far enough north and south to get a wide variety of fruits. Not sure if they will have a large fishing fleet or anything, but assuming the empire is potentially overpopulated, we can assume they make an effort for such things, thus potential scuffles with the Republic just to the north.