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I don't think this is the case. Putting my phone in silent doesn't activate the mute setting in the glances screen, and I still get sound when I get activity notifications.
 
No, but I wish they did do this. You can mirror the iPhone settings for a lot of things (like Airplane mode), but this is not one of them.
 
No, using the mute switch on the phone doesn't silence the watch, but you can mirror do not disturb from your phone. You have to mute the watch by using the control center glance.
 
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