I think both android and iOS supports decreasing the badge number on an app through special push messages, so that if you clear your notifications on another system you can send updates to the mobile app so it decreases or hides the badge number. It’s probably a good idea to limit the update rate though.
I don’t think anyone expects just reading the native notification to update anything without opening the Discourse app first. Personally I would find that annoying, because sometimes you mistakenly clear all your mobile notifications or the phone does weird things, I wouldn’t want that to be reflected to websites automatically.