How are they served? How are they kept? Well, I dunno 'bout in the civilian sector because I avoid them like spore molds, the plague and a BMI above normal range, but I can provide the military perspective on this shit.
A'ight. So yeah, these fuckers are frozen. And they're maintained frozen. There's large freezers onboard aircraft carriers with special fucking shelves dedicated to uncrustables, as they are a staple of life for sailors.
See, (almost) every aircraft carrier has very set messing hours. By messing hours, this means the hours the mess decks are open and serving meals. (I was onboard one that had nearly 24 hour hot food, and it was glorious - however, that was first ship, and every ship after cut off service, making 4 distinct meal times (the 5th was just for watchstanders in Reactor Department, because those poor fucks were stuck in the plant during midrats (midnight rations) and couldn't get a meal if that was the rotation they were stuck on). Those meals are as follows:
Breakfast
Lunch
Dinner (which may be lunch again)
Midrats (which is dinner. Nothing new. Everything reheated.)
And then Reactor Rats (which is midrats that were set aside for the 80 watchstanders stuck wailing in hungry agony in the plant).
So what is a Sailor to do if they can't make these meal times and/or the mess decks run out of fucking food (which does happen, because they do things like forget that Reactor Rats are for only Reactor Department and give them to any schmuck who wanders to the galley and sees food and asks for it, therefore resulting in shortages by the time half the watchstanders in the plant get to main deck for food)? Hit the 'always on the mess decks' options. This usually involves fruit which may or may not be fresh and might consist only of red delicious apples. Usually there's some nutrigrain bars or an equivalent there. Every now and again, wheat PopTarts will appear. Cereal can happen, but normally is stored outside of breakfast otherwise it tends to walk off the mess decks and be hoarded in offices.
Uncrustables are one of these 'always out' foods. Except they vanish VERY quickly.
They're put out, usually frozen because nobody can be assed to defrost them before putting them into the metal tray of availability, and snagged instantly. From there, it's up to the individual. Most Sailors I knew would toss them onto a desk, into their storage locker or into their coffin rack and save them for desperate times, allowing them to defrost quietly without issue (and what's freaky as fuck is that I never was privy to a moldy one. Even one that got left in my LPO's inbox for 3 weeks just got crunchy. Never moldy). Others, desperate for food /right fucking now/, would microwave them for a few seconds. Some did the same I did when desperate for calories after 5 hours of labor in the plant - plunk them into the conveyer-toaster and get them hot and lightly toasted. That was the only way I personally found them tolerable.
Now because all that was reliable on the mess decks was squishy apples and water during those hours that the galley wasn't in operation, uncrustables vanished quickly. This is where the Chiefs came in.
See, the Wardroom (home of commissioned officers) and the Chiefs Mess are off limits to lower enlisted (E6 and below), which make up the vast majority of the ship's workforce. So some of us who had access to these places would do what we could to pass on the goodness, so to say.
I will say that the fruit available in the Mess was usually pretty well received, but nothing would get glee from a junior Sailor quite like a bag of fucking uncrustables. I have no idea why they were so attractive to my kiddos other than 'they keep forever in a desk drawer and are there and waiting when true hunger strikes after watch and the fucking mess decks are closed.'
Don't ask me - when I was the most junior of juniors, I was on the 24-hour-open-messing ship. After that, I survived on coffee and hatred until I made Chief, and then I became the Bearer of Uncrustables for my Sailors (started when one of the kids in my workcenter very timidly asked if they had uncrustables in the Chiefs Mess because they were out on the enlisted decks and he missed dinner. I checked, found the storage repository, and all else is history).