It might be worth considering that an apocalyptic scenario doesn't necessarily mean every inch of the land has been nuked. So we don't have to worry about whether or not something would survive ground zero. Just whether or not you could happen across a functional gas powered rifle with or without ammunition in the year 2280 under a reasonably well covered nuclear experience.
Before we worry about finding weapons in special containers designed for century long sleep, perhaps we should consider who survived the initial apocalypse, and what the journey of these weapons may have been.
A quick example, suppose you had a character on a homestead in a remote Alaskan compound when the event took place. This person is pretty sure this is what they have been prepping for since forever, and they hunker down and play one-man army by themselves and their consortium of like minded preppers for say the next 20 years or so. During this time, nothing happens. The apocalypse has shifted people's interests and for whatever reason, nobody cares to hunt down stockpiles of weapons and food in remote areas with secret compounds. So these preppers have lived a fairly uneventful apocalypse, far from the fantasies that made them stock up on 20 years of underground supplies. But a prepper is a prepper. Generationally, they teach what needs to be done to who needs to know. Their weapons are never neglected in the entire 200 years you speak of. They are maintained, passed down, and stored how they should be. They just never happened to be required for combat survival, and so their general wear is not expected to exceed much beyond common handling, and the occasional neglectful slip up that means they are no longer in new condition.
The point being, you can find a 200+ year old weapon in perfect-ish operational condition if the back story is sufficient. It doesn't have to be found in a crate. It can be a trade for a truck or something the owner needed and was willing to give up an heirloom rifle they have never needed, and still have 50 more in their bunker. That part is up to you.
The ammunition thing - I mean, people will want to argue all day about what will and won't work here. But it's your story. You can allude to survivalists who have gone trough great strides to preserve this technology to a certain point, and remove them from the tale at a point where it still serves your interest. Like finding a makeshift ammo plant that was operated by the survivors who knew what they were doing, but eventually bit off more than they could chew and died off having exhausted their wealth of ammo down to a paltry 100,000 remaining rounds. A tiny number to the military, but a lifetime to the right camp of post-apocalyptic survivors. Maybe this happened 20 years ago, in 2260. Doesn't matter. You found functional 5.56 ammunition to feed through your AR-15s and other weapons using that cartridge. Have some jam, fail to fire, fail to eject, fail to feed, squib, and it is reasonably believable. (BTW, look into ammo squib. That seems like a very plausible point of interest in old ammunition for stories like this. Could blow your face off)
This is the approach I would take, personally. I believe most weapons people find 200+ years after manufacturing of any weapons ended would be the ones scavenged at the beginning and cared for by the survivors in any generation. If not the beginning, then within a reasonable time frame before nature started taking back the structures and covering the hiding spots well. There are plenty of enthusiasts, private organizations, and braniacs who will have thought to prepare for this, and will have the means for rebuilding caches of ammo outside of the typical industrial methods we use today. And everyone dies eventually. No matter how well prepped you are, in the end it's perfectly believable to imagine the life path of a settlement who was there in the beginning to eventually, over the generations, reduce all the way down to one old dude in a hut, sitting on top of a bunker full of things he had nothing better to do with than clean, preserve, organize, document, etc. Right up until the day he died alone at age 55 in the year 2247. 12 years before he was discovered by some hippies caravanning or however you want them to be unearthed and ready to find their way into the hands of your characters. Maybe even with some basic care instructions.
It may be the apocalypse, and it may have hardened people, but it is not beyond reason to figure that some would actually work to preserve the means to survive, and be willing to teach others, and not just scavenge and stockpile found weapons and ammo. It wouldn't be as efficient and high tech as today, but it doesn't mean it is impossible or even outside the realms of plausibility to have ammunition generation continue as far as you need it to, even all the way up to 2260 and beyond if it serves your story right. Don't forget, if anyone snarkily asks where you happened to get a hold of some ingredient to make and stabilize your primers or something, you don't have to explain. You can just say we ran into a guy. Wouldn't say where he got the stuff but he was very interested in trading for a few lithium plates.
Hell, even Andy Weir didn't go all the way down the rabbit holes for the Martian. Even he cut off the details in favor of an occasional "because NASA" or something like that to forgive the need to science the F out of every bit of the story. And it works well. Too much detail might interfere with the story more than bolster it.
