To answer your question
If you assume you are providing 2 decks about 2.5m each, that gives you 5000m^2 of ground space. If we are also not too concerned about humane treatment, then you need about 2.8 m^2 per goat of living space. We can also vastly reduce grazing space with hydroponically grown grasses which can produce a theoretical maximum of about 19kg/m^2/yr. Each goat needs about 500kg of feed a year meaning you only need about a total of 29m^2 per goat. I will actually estimate this closer to 35m^2 per goat because you also need to account for things like walk ways, food processing spaces, veterinarian spaces, supply storages, etc. allowing you to maintain a herd of about 45 mothers, 90 calves, and 5 studs. If you assume you are slaughtering about 80 calves a year, that is about 5-6kg of meat a day... or if you are not raising calves for meat, but just enough to replace attrition, you could have closer to 120 milk goats, 15 calves, and 5 studs for a dairy production of up to 120 gallons of milk a day. Milk itself is mostly water, but if you wanted to process it into cheese so that you have a meat substitute, then you would get 43.5 kg of cheese. So lets assume you want meat, cheese, and milk for a nice varied diet, you can produce about 3kg of goat meat, 19kg of cheese, and 30 gallons of milk a day.
Since the average person eats 100-300g of meat, eggs, and cheese a day (depending on cultural preferences) This would be enough to feed a crew of about 180-530 which should be plenty given the size of your crew compartment.
But you should also include fish tanks
There is a livestock that is much better than chickens or goats: fish.
For starters, fish is rich in Omega-3 fatty acids which is one of the few essential nutrients that your body can not produce from other sources and is really hard to get out of a vegetarian diet. You need it to maintain good health, and fish have it in much higher ratios than other meats; so, you can maintain a healthy lifestyle eating less meat if the meat you are eating is fish.
Secondly, they need much less feed because they are mostly sedentary, cold blooded animals. It only takes 1.6kg of fish feed per 1 kg of meat making fish farming ~3-20x as efferent as other common sources of meat. Furthermore, fish can be fed algae which grows MUCH faster than grass the grasses you need to feed goats and chickens. Agriculturally grown fish could use this same space to grow about 500kg of meat per day making them ~83 times as efficient as goats for meat and ~12x as efficient as goats for milk.
So I'm not saying you can't do chickens and goats in this space since you've allotted enough room given the right techniques, plus they may be seen as good for your quality of life, but you may want to consider adding fish as a major protein source to reduce your total livestock space requirements. If just 60% of your protein requirements were met by fish, you could reduce the amount of space needed for raising livestock by about 1/2.