Given that the OP has added or clarified a condition to the question:
You are too focused on food and livestock. While I indeed need to feed
my crew, I need organic matter for other reasons, too. Moreover, I
need them to be as close to original as possible. For example, I need
most of the DNA and proteins intact and easily accessible for
manipulation in many ways. You correctly identify problems associated
with keeping animals alive while in a coma, but you ignore all
chemical changes to dead tissue. I also realise that this whole topic
of keeping organic matter intact for long periods of time is highly
underappreciated and people tend to oversimplify things.
Alive is the Only Way to Go!
Since you need to be able to access and manipulate DNA and other biological materials, in addition to having access to crew rations, the best solution will now be twofold. Storage of frozen food for long periods of time has already been discussed (focused on meat). But you will also need a way of preserving living tissue. The best way to accomplish the feat is to keep partially prepared food in the deep freeze as already discussed but also to step up keeping live plants and animals in some kind of habitat.
You could consider, as part of ship design, a large free range biohabitat. Stocked with small livestock such as chickens and rabbits and an appropriate predator species, its environment monitored and adjusted by ship's AI, your crew might just awaken to fresh fried chicken!
This is unlikely to work long term, as disease will be problematic and population spikes and catastrophic dips may lead to extinction of the biohabitat. While balance issues may pose tricky problems, at least the time span is short enough that you might be able to pull it off.
At journey's end, the biohabitat will contain sufficient biological matter, in the form of living animals and plants as well as decomposing matter and compost that can be used for other purposes, such as manipulation in order to grow artificial meat or to make pharmeceuticals, vitamins, hormones, etc.
The advantages to the split system are numerous: you will have fresh food available to the crew upon awakening; you will have a ready source of biological matter onboard; you will also have something approaching a natural habitat for the crew to enjoy while performing onship duties at the end of the journey. Even though you propose a very high level of technology, you don't have synthesisers capable of extruding complex biological material. A biohabitat (or two) will solve the issue of "preservation", because nothing beats a living plant or animal for providing biomatter.
Although we discussed keeping animals in a coma, inducing a state of torpor will pose similar problems. The main problem is the simple fact that animals are mortal creatures. They have a basic life expectancy that very few will survive, and will be almost impossible to overcome while incapacitated and supported by machines. Barring some kind of "stasis field" technology, there is just no way to "store" a plant or animal and ensure that it will continue to exist, in a living state, beyond the capacity of its kind. The life span of many crop plants -- tomatoes, lettuce, etc is literally a year. Though others may last much longer -- grapes, apples, other fruit trees. The life span of food animals rarely exceeds 20 or 30 years. This is the insurmountable problem of any kind of "storage".
The advantage of designing biohabitats into your ship is that the plants and animals will exist in something approaching their natural state. The biohabitat will have night and day cycles, can have seasonal cycles, can have artifical weather conditions and will be self sustaining, once fabricated.
The good folks over on Cooking.SE have asked this very question. The long and short of it: properly prepared meat (raw, vacuum sealed, maybe irradiated, kept frozen (0 deg F)) can last indefinitely.
This Woman's Day article about freezing meats quotes an FDA fact sheet about freezing foods. The pertinent language reads: "Food stored constantly at 0 °F will always be safe. Only the quality suffers with lengthy freezer storage."
Quality suffers, according to a comment within the C.SE query, thus: Generally, meats dry out (freezer burn) when frozen before they become unsafe to eat. You can reduce the drying effect by double-wrapping meats, and a vacuum sealer is especially helpful. Freezer burnt meats become tough and grainy, but can normally still be used in stews, stocks, and other preparations that hide the damage. (Bruce Alderson)
I think 200 years of cold storage should yield an edible, if not terribly palatable, meal.
But what about living tissue? Living tissues can indeed be kept, though not really "preserved" for a long time. This process is essentially an induced coma. Essentially, the person in a coma exists in a state of deep unconsciousness. Presumably, an animal placed into an induced coma would similarly exist in a state of unconsciousness.
The record for longest coma is something like 37 1/2 years. Not quite long enough for your purposes! The main problem with this kind of storage of living tissue, whether human or animal, is that the body continues to grow & develop. At least to a point. People in comas are not in any kind of "stasis" -- they are still susceptible to environmental diseases and may still develop cancers. Finally, no living thing this side of the veil is immortal: a person in a coma will eventually die. Most likely from complications of the coma itself; but at the last, even a comatose person will die of old age.
There are plenty of bad things that can happen to a comatose person, ranging from infection to decreased bowel and respiratory action, lowered blood pressure, bed sores and atrophy from disused muscles. A food animal stored in such a way would almost certainly suffer the same physical degradations. This is not a viable alternative for the simple reason that it's the muscle tissue of the animal your crew will be hungering for when they wake up at journey's end!
Dead tissue: one time Earthside preparation including initial butchery, multipacking of raw flesh with irradiation & vacuum sealing, rapid freezing. Shipside requirements: freezer units that are accessible to crew upon waking. Ship's AI should be programmed to monitor temperature and perhaps vacuum conditions of the freezer units; should also be able to quarantine a/o jettison compromised or nonfunctional units. Results: guaranteed.
Live tissue: livestock animals will need to be initially processed (bathed, decontaminated, quarantined) before entering Earthside facilities. Once there the animals will be anesthetised, cannulated, unconsciousness induced, intubated, and loaded into harness cradles. The harness cradle serves as a suspension storage apparatus with attached medical grade machinery (respirator, multicapacity IV pump). Shipside, the suspension cradle will be attached to the on board MPS (meat preservation systems), which will include all necessary lines to central storage facilities, including room air, oxygen, potable water, IV nutrition, IV fluids, and an assortment of pharmeceuticals. The MPS will also feature a physical (passive) exerciser (an attempt to preserve some muscle mass); a total waste management system (handles poop and pee, sending them to the central recycling unit. The MPS units, of course, must be kept in an inhabitable part of the ship, with appropriate environment constantly monitored and adjusted. Ship's AI will be programmed to monitor the basic health status of each livestock animal (ekg, blood gases, respirations) and must cull & jettison deceased animals. Cows live about 20 years. Results: this was a bad idea! Reason being, once your crew wake up, they'll discover that the entire herd of induced coma cattle are long since dead and jettisoned.
Dead tissue presents far fewer challenges as far as storage & maintenance go. Live tissue requires what amounts to 24 hour health management of each livestock animal. In addition, the effort will be wasted since even the optimal lifespan of the livestock animals falls far short of the journey's expected time.