In fact, at our shops, on older iPhones, I can test the battery state by opening the camera app. If it takes 10-20 seconds to open, it’s usually the battery causing it. (The other cause is storage being close to full.)
This won’t help the app resetting issue, which the author correctly identifies as a RAM problem (that I also encounter on my personal iPhone 13 Pro. Apple is horribly stingy with RAM even on the Pro models.)
In general, if you use your phone daily, I recommend getting the battery replaced every 2-2.5 years.