I don't think food is going to be so bad. Creating farm habitats in space is something we could do already with present day tools, assuming we had infrastructure in space, which folks in Starsector certainly do have. Creating fertile earth and breathable air is also just a matter of time and resources, not technology. Just break apart some carbon and ice asteroids, scoop some nitrogen from the atmosphere of whatever planet, stir it all in a rotating cylinder with some hardy microbes and wait for it to become fertile enough for plants. Even if we ignore the space habitats route, we still have to note that there exist multiple planets that can be dedicated entirely to food production. Making enough food is not an issue.
Herbivore domestic animals, while becoming relatively less important, will most likely still exist. People can eat some parts of plants, but not all. The remaining parts can be composted, or they can be fed to farm animals. The latter part will still provide compost later (after manure has been processed) and what is useful is that it has different properties to plant waste, so there might be some demand for it in the future. The second reason you want actual animals is milk. Well, maybe want, maybe not; it's hard (for me) to say if "animal milk" is meaningfully different from "plant milk". Presumably it might remain viable to some extent as traditional or luxurious alternative to mass-produced and cheap plant milk. The third reason is meat and most of reasoning is the same as for milk, though with the caveat that we still don't know how viable cultured meat will be. The possibilities range from "so bad, you don't want to eat meat at all" to "genuinely better at everything, except for the inedible parts". For Starsector, I'd like to shoot somewhere in the middle. Regular people can eat animal meat as often, as they did in the ages before industrialisation.
What I would really like for Starsector lore to do, though, is abandon this generic "we will eat mystery sludge in the future!" route for more DRM magic. Imagine if it got to the point, where there are oversized vending machine abominations in place of restaurants that grow, prepare and serve the food, all in one. Not just any food, though, only the special, corporate-approved McSpace McBurgers and McSpace McFries. Or Agricultural Intellect's finest vegetable and cheese Rye Rolls! So many foods, conveniently available anywhere... With the only caveat that various food companies own them all and they are quite protective of their designs. And that people got so used to them, they forgot how to prepare some (or even most!) of these foods on their own. And that various blueprints after the collapse might have been lost, so certain automated restaurants or vending rooms are irreplaceable and quite valuable, even if they are nothing special. And people are too busy fighting to fix all this stuff. And those companies that made those designs might not have made them... Completely free of side effects, for whatever the reason. Or that current factions do that. Suddenly, having a cow or a tree you can't just hack seems more appealing.
I feel this is more interesting take on food scarcity.