Normally a fish jumping out of a pond that has new water is pretty standard. People cover new ponds and temp tanks with netting to prevent that (future reference).
Gasping for air can sometimes be normal. It's hard sometime for people to tell, but it sure sounds like your fish are really gasping.
Fish not eating, assuming the water temp is pretty high (above say 40F) is not a good sign. Fish listing is a really bad sign, like not going to be around tomorrow type bad.
So in this case all the sometimes normal symptoms all point to a real problem. They can't get air. They can gulp air for awhile but not long term. May in WV I assume the water isn't super hot so I assume the O2 level in the water is fine. I wish I knew when the fish jumped out of the pond in relation to being put into the pond. Because of the other symptoms it's a pretty good guess it jumped out because there was a problem with the water and it wasn't "normal" jumping.
The pH may have been an issue. But in general dumping fish into water with a much different pH is more of a stresser. It can kill fish outright, but not often. So it doesn't sound like pH. And besides at this point testing the pH doesn't help much because you don't know what the original water was so you can't try to match pH. Beside, its been 5 days. They would have adjusted by now unless the pH is really insane. The last thing you want to do now is start dumping stuff into the water to try and change pH.
What fits better to me is their gills have been damaged. From chlorine in the water. I don't know what the "algae control" was but maybe that, or a combination. I don't know what 'water safe' product you used "to clean the chlorine" but I'd guess that was the problem. The barley could be adding to the trouble. The thing about barley is it could be anything. Not like there's any kind of regulation about what is in a barley product. It's a wildcard.
The fish have only been in this water 5 days and these symptoms started some time ago, water is probably pretty cool, so I wouldn't guess ammonia, but it certainly should be tested regularly for a pond that size...but I don't know what size the fish are, or even if they're Koi or Goldfish, so can't say how important ammonia testing is. But I'd guess important.
Sure doesn't sound like spawning. Gulping air doesn't help their mood. And the swimming behavior doesn't sound right. But I'm only going by what's written, I can't see it.
Other outside chances would be there was an ammonia problem in the temp tank and that damaged their ability to use O2.
Being in WV I'd have to wonder if the tap water is a problem. You all just had that whole poison water thing and I see they just raised the amount of selenium they allow from coal runoff. It doesn't really sound like WV cares much about water quality. So that could cause the water provider to really push water limits, like adding a lot more chlorine or screwing with pH to try and make water safer. Those things can be a problem for fish.
I kind of hate to suggest fixes. The problem is you haven't been testing water so no idea what's what. Adding stuff like "water safe", algae control, barley without knowing those things are bad for fish is a red flag, so I'm very afraid if I say add this or that and a bunch of other people say add that or this that it's really going to be bad. These things aren't simple to fix. If it was chlorine the chlorine is now long gone and the gill damage is done. That doesn't really get better. So I think the pie is already baked.
I hate to even say it's time to start thinking about putting the fish down because I'm I'm just reading text.
I think it's best just to let them be and see if they pull through. But this is an excellent time to consider learning more about fish keeping for future issues, future fish.
My best advice for the future is to never ever use these bottled products. They say very misleading things on the front label while the fine print tells you it's toxic to fish. And very few actually work for most ponds because either they're a scam or people don't follow the directions perfectly. That includes barley. Be really, really careful where you get info. Unfortunately there is a lot of bad info. So the safest thing is don't use products less you've read the MSDS and really have a good understanding of what they do to fish and the water. And if you don't then just don't use them. It's not like they do anything useful anyways.
For example, to make sure chlorine is gone use a chlorine test for swimming pools. Yes it means you might have to wait a day, a week before adding fish, but it's way, way safer. Besides that waiting period can improve other things. And the test probably costs less than the "water safe".
I do hope they pull through.