This is not an answer, but rather my thoughts on the subject that I decided to share after getting initial responses to my question.
There are three main considerations when it comes to food preservation:
- nutritional value (macro- and micronutrients);
- texture and taste;
- presentation (colour, serving sizes, decoration, etc.)
Available food preservation techniques negatively affect all three aspects. Nutrients are destroyed during preparation for storage and during storage itself, texture and taste may be altered, and presentation may suffer greatly as well. I was looking for ways to negate (to some degree) all three as food is critical for the physical and psychological well-being of humans, especially in space.
Macro- and micronutrients
Preservation of nutrients is the most important aspect since there is no external source that could provide missing ingredients. As we know from history and modern research, nutrient deficiencies lead to deterioration of physical and mental health and ultimately death.
While there are some types of food that can be stored sufficiently long for my purposes, they would not constitute a balanced diet. A non-exhaustive list includes raw unfiltered honey, soy sauce, refined sugar, salt, white rice (some varieties), cornstarch, vinegar, pure vanilla extract, low-oil grains, dried tea leaves, cacao, and powdered milk (if frozen).
My research of modern food-preservation techniques (canning, freezing, irradiation, dehydration, controlled atmosphere, chemical additives, fermentation, extraction, and so on) suggests that none of those methods is effective for long-term storage measured in centuries. While it is possible to preserve macro-nutrients, especially, carbohydrates, the degradation of micronutrients, most notably, vitamins poses a big challenge.
Willk's proposed answer is based on the use of these techniques and their combination. It is a good common-sense approach, but it ignores evidence that, for example, blanching is necessary before freezing for many plant-based foods. Blanching is a heat treatment (may reduce Vitamin C content up to 90%) that deactivates enzymes responsible for certain types of food degradation. Enzyme activity does not stop even if food is frozen, it only slows down. Moreover, enzymes become more active during defrosting. (Humans cannot consume all food frozen, so defrosting is necessary and should be included in any discussion of food preservation for later consumption.) Likewise, irradiation and dehydration also lead to the loss of nutrients.
As discussed with DKNguyen, freezing also does not stop the deterioration of nutritional value. Vitamin C, for example, continues to degrade at freezing temperatures (-20C). The loss of nutritional value in cold storage as shown in the linked source is negligible when we store for 6 months. However, losses accumulated over a period of 2-3 centuries may be very significant. It is likely that rapid freezing and storage at near absolute zero can arrest some of this deterioration, but so far there is no scientific proof for this.
Freezing also causes denaturation of proteins, which affects some groups more than the others. This may have negative effects on nutritional value and digestion. More research on my part is needed to clarify this in greater detail.
Some commenters suggested using dietary supplements to make up for losses in the nutritional value of stored food. This seems like a reasonable suggestion, but it may pose problems due to bioavailability and drug interactions of the said supplements. Micro-nutrients in food and pills are not always chemically the same and are not processed by human bodies in the same way. Dosages should be calculated very precisely and depend on a big number of factors such as genes, microbiome, diet, and even mood. It is also observed that multi-vitamin supplements can increase the risks of cancer and cardiovascular diseases.
I am going to do more research, but it seems impossible to preserve the nutritional value of food at high enough levels with contemporary or slightly more advanced technology. Some supplementation is necessary. It also looks like crew members would require close observation and individualised solutions until food production is fully established to prevent nutritional deficits.
Texture and taste
Texture and taste are extremely important. If people do not like them they are not going to eat their food or not going to eat enough of it.
Food texture is often downplayed or completely ignored, but it affects taste a lot and for many people is a decisive factor in food preferences. I, for one, cannot eat anything resembling porridge: a sticky substance with pieces of something more solid in it. Even thinking about it makes my stomach sick. Moreover, the awareness of food texture is often subconscious, so it may have a profound impact on the perception of food and psychological adaptation and well-being of space travellers.
As for the taste of food, astronauts report that it changes in micro-gravity. This, most likely, can be attributed to physical changes that happen to human bodies in such conditions and loss of sense of smell. Some astronauts complained that sweet food, especially with added sugars, was too much for them. It is also known that spices and spicy sauces are very popular on ISS as they help to overcome the blandness of the food.
Food preservation techniques often lead to changes in texture and taste. Some of them are intentional and some are not. Unintentional changes are usually related to the cellular and molecular damage resulting from preparation for storage, storage, and preparation for consumption (defrosting, hydration, etc.).
Ice crystals formed during freezing (even rapid freezing produces ice crystals, albeit smaller) damage cell walls. This reduces firmness of the fruits and vegetables and leads to loss of nutrients and altered taste due to drip loss. The scale of damage depends on freezing methods, species, and specific cultivars.
Freezing also causes denaturation of proteins, which is especially damaging for animal-derived food. For example, frozen fish may lose taste, change colour, and become tougher. This process also reduces the bioavailability of proteins, thus diminishing nutritional value.
Damage to the packaging of frozen food may lead to the loss of moisture and 'freezer burn'. While it does not make food unsafe per se, it makes food tougher and creates eating experience akin to chewing leather or wood. This is highly undesirable in an already stressful environment.
Presentation of food is another important aspect of preservation. Food that tastes great and has high nutritional value still will not be consumed enthusiastically if it does not look good. Shared meals are also important for morale and teamwork.
This is something that I still need to research. Of course, there are limitations on serving methods available in micro-gravity and a restaurant-style meal would not be possible even if I could teleport it to the ship. I still believe that it is possible to come up with something that will be more exciting and pleasing to eat than nutripaste or soylent green.
At this point, I am leaning toward freeze-dried food rations kept at near absolute zero supplemented by permanent algae and yeast farms. Algae and yeast cultures are relatively easy to maintain, so this can be done by automatics and supervised by the emergency crew members in extraordinary circumstances. Algae and yeast also have a benefit of easier storage and farms can be scaled up as demand increases. There should also be fewer problems associated with micro-gravity. An additional benefit is that algae farm is a proven technology not just for food, but for other life-support systems, and it was already included in my world design.