If you can keep it free of moisture and free of oxygen, many foodstuffs will last a decent amount of time.
I recall reading about tins of meat packed in lard that had been sent to the former Soviet Union as aid from the USA during WW2, that were discovered sometime in the 2000s on old battlefields. The meat inside was described as appearing fresh enough to eat (although, apparently, none of the people who were testing it had the desire to eat 60 year old meat).
The constant cool temperatures in that part of Europe had ensured the lard remained solid and in that state, it kept moisture and oxygen from the meat and prevented it from rotting.
Another example from 2012, the New Zealand-based Antarctic Heritage Trust found a well preserved fruitcake when they were carrying out restoration work on a hut used by the Scott expedition of 1910-1913. The fruitcake was 100 years old and described as being in excellent condition.
Again, the environment of the area played a big part, constant cold weather with low moisture content.
https://www.nationalgeographic.com/n...tt-terra-nova/
And according to this article, the actual shelf-life of freeze-dried food that is canned can last up to 30 years and not the five years typically advertised as the use by date.
https://funfactz.com/food-and-drink-...d-safe-to-eat/
Speaking as someone from the Australian military who while on exercises in the field was living on ration-packs that were anywhere from seven to twelve years old, I can attest that many foods will last much longer than people generally think.
Other articles worth a read: -
https://www.dailymail.co.uk/femail/a...sell-date.html
https://www.asgmag.com/prepping/food...vival-rations/
As mentioned in other posts to this thread, many of the above linked articles mention that the mineral content and overall nutrition content did degrade with age but the food was still considered safe to eat even if the taste was a little off.
Given those examples, I think it's entirely feasible that the Project could have created preservation techniques for the long-term storage of food by imitating those same low oxygen, low moisture environments and if they could keep those foodstuffs at a constant temperature during storage or even better, keep them at a constant cold that would likely lengthen their storage life a good amount.