I'll explain what I put in my first post a little further.
Years ago I called and spoke with a chemist at the company that supplies Ace Hardware brand Janitor Strength Ammonia. It is a 10% solution, nominally. He told me that they often add small amounts of ammonia to steel drums filled with water to prevent rusting in the drum. But that was a tiny amount, and probably just enough to bias the pH slightly above 7.
The 10% solution is right on the borderline for etching steel. Back about 1990, I had a .308 Redding FL sizing die I'd got a case stuck in and that the head tore out of when I tried using an extractor. I set it in the 10% ammonia solution in a glass jar to eat out the brass. It took about three months. After that time, the surface of the die looked gray. It was clearly micro-etched and activated, as it rapidly formed surface rust. I needed to polish it lightly, but it worked fine. There was not enough etching to change its dimensions measurably, even after three months.
I also spoke with the maker of Butch's Bore Shine a few years back. It's ammonia is not as concentrated as Sweet's, but it is still pretty strong. He told me they had put a bar of 4140 steel into a jar of Bore Shine for six months and inspected it for surface etching under a microscope afterward and found none. So it is either safely below the etching threshold, or its additives control it better. It is a good copper cleaner that I can recommend if an ammonia cleaner is how you want to go. I used it for a number of years with no problems. I have pretty much switched, now, to the Boretech Elimenator for metal fouling simply because it works faster and leaves a corrosion inhibitor behind when it dries, so, even though it is water base, you can leave it in a bore. I also use Gunzilla wherever carbon is the main problem, such as in shotguns or in detail cleaning. It is vegetable oil based. It is also one of the few cleaners I've ever seen actually soften carbon cake over night, such as you see on a Garand op-rod. Neither product is toxic nor do they leech oil out of your skin. Gunzilla leaves a thin, dry lubricating varnish-like surface behind. The military has apparently adopted it enthusiastically because that feature reduces malfunctions.
Sweet's, on the other hand, is what I had been using until I found surface rust in my M1A barrel one day, also in the early 90's. I don't know if that is because I'd failed to follow up with my usual patch of LPS-2 (Birchwood-Casey sheath is the same thing) or what? Some error of mine was clearly involved, as that was not normally a problem. So, Sweet's may be a tad too strong if it isn't removed. I also experimented with a lot of cleaners back then, so it is possible I mixed a couple by using one then the other in the bore when I should not have. I didn't keep records of that, and was kicking myself afterward when I tried to figure out what had happened? So, I can't blame Sweet's with any certainty.
You can take PDGXS's suggestion to follow up ammonia with a patch wet with hydrogen peroxide solution. That will drive off any remaining ammonia as gas, but it also supplies oxygen which will promote oxidation if there has been any surface etching. I think a better way to insure all the ammonia is gone is to use the black powder shooter's method of pouring boiling water down the bore to drive the stuff out. After that, flood it with WD-40 (Water Displacing formula number 40) to remove the water. Then remove the WD-40 with a couple of dry patches and finish with a patch wet with gun oil or the storage lube of your choice. WD-40 gets a bit tacky and attracts dust if you leave it on something.
If you discover you've got a bore that rusts easily, use Flitz on a patch or use JB bore compound or Remington Bore Cleaner or Iosso Bore Cleaner, or any of the slightly abrasive cleaners to polish it lightly. That will clear off the activated surface.