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Press the crown button. Watch apps are really just extensions running on your phone and shut down whenever they're not in use.
 
The watch does not need to be micro-managed like a desktop computer. Even the phone, to be honest, doesn't either. I never "shut down" an app unless I think it's misbehaving some how.
 
There is only one App running and this App transfers the WatchKit Extension data from the phone to the watch.

There is no code running, except Apples own infrastructure code for WatchKit Extensions.

Therefore there is no reason to stop anything.
 
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