As others have said, the lack of sunlight on the surface (as well as the ease of which the machines could attack above-ground human settlements, which is why Zion is subterraneous in the first place) rules out any natural, above-ground farms. As to why there are no apparent farms lit artificially in Zion, space constraints are the likely reason. Farming wheat, carrots, onions, etc on the scale required to feed a large populace requires quite a bit of space and water.
Despite the difficulty in keeping a self-sustaining farm in the confined space of Zion, with it's limited resources, I suspect they do have some sort of array of crops. The most likely candidate would be hydroponics grown crops, as they would not require viable soil (most of the topsoil on Earth has likely been corrupted by the machines, as a result of the massive pollution their civilization would incidentally release, which they would have no motivation to limit), and would also not require crop-rotation (which would be difficult with Zion's space constraints). It is likely that their selection of crops to grow is limited however, I doubt that when humanity fled the surface of the Earth it was able to bring a large quantity of seeds from every type of plant crop (though whichever government effort led to the inception of Zion probably planned supplies of plant seeds as well).
Regardless of the method of which Zion grows crops in theory, it is very unlikely that Zion only eats the "single celled protein combined with synthetic aminos, vitamins, and minerals" porridge, as I would point out that although the amino acids, vitamins, and minerals are said to be synthetic, that does not mean they magically appear out of a machine with no source. Unless they literally have technology that takes raw elements (Copper, Hydrogen, Carbon, etc) themselves and forms them into larger biological components (something that I've not heard of being feasible even today, and if it is, it would most definitely be terribly inefficient), it's likely that they are extracted from food products.
It's easier to specifically answer why the crew of the Nebuchadnezzar and other human ships had to eat the "bowls of snot". Where it is challenging to produce a sustainable farm in Zion itself, it is even more so in the limited space of the ships, who also do not have access to large, replenishable sources of water. In reality, NASA has experimented with self-sustaining hydroponics on it's shuttles, but they are not close to being primary food sources, and are more a novelty to study at the moment. Even if the Nebuchadnezzar could house a hydroponics bay large enough to feed the crew for voyages that could be weeks to months long, it would be very vulnerable to disruption. Think about how frequently the Nebuchadnezzar is forced to stop and shut down all power for several hours (and possibly a few days in the rare occasion that there's a buildup of drones in the area). During that time, the water aerators would not be oxygenating the water nor would the temperature be maintained at the level required for the plants. And even if they somehow had more resilient hydroponics technology, what if the very real possibility of the Nebuchadnezzar being scuttled by it's own EMP, or even a simple malfunction, came to happen? The hydroponics bay would most definitely fail within days (and refrigeration of any crops would fail).
As such, keeping a colony of simple single-celled organisms is an ideal substitute for crops on ships. Such a colony would only require that the temperature not make extreme fluctuations, that water levels are kept constant, and depending on the organism, that sugar or starch (or even alcohol, some species of yeast can metabolize alcohol under less ideal conditions) be regularly provided. Reliance on electricity would be minimal to none at all. Interestingly, the "snot" produced on the Nebuchadnezzar is evidence that humans have crops somewhere (in Zion), as their single celled colony still requires food from some source. This indicates that they possibly grow beets, or sugar cane, or some good source of sugar or starch, as either would be needed to support the "snot colonies" on ships.