I've seen people say that even spoilage times of years cause problems in large servers so I definitely think there should be some "final" tier of food that just never spoils, and would be more convoluted to make.
For Fruit and Vegetables it should definitely jarred Jam and Pickles if glassworking is ever added, maybe requiring propervacuum canning in order to fully preserve them.
For Protein I feel like Jerky is a common enough suggestion. You can cure meat, so you'd also be able to smoke it, and if you do both youbget jerky. But it feels way too simple for it to be the most advanced produce of this type, so I was thinking, what about sausages? They also require both curing and smoking but they'd be more complex to make, requiring lumps of fat as well as scraped hide for the casing.
For Dairy, Parmesan Cheese, though I don't know enough about it to know exactly how its production would differ in-game from Cheddar/Blue Cheese. Maybe unwaxed cheese would need to be aged in a cold enough cellar to age into Parmesan, but if it was too warm it would spoil.
I don't know what Grain would be, Hardtack seems realistic but it'd be way too simple, and giving nutrition to Ale feels weird. Sealing raw grain in crocks could work but I feel like the final tier of food products should be ready to eat right off the shelf. Maybe some kind of cracker or cookie
The biggest reason I want this though is just because the thought of having a cellar stocked to the brim with fully developed foods that took a lot of effort to make and will never spoil sounds like the most satisfying feeling ever.