Silent mode
When i put my watch on silent, it continues to still make my notifications sounds. Even when both my phone and watch are on silent, my watch will still ding. This seems to be hit or miss at times too.
Apple Watch Series 4, watchOS 5
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Do you use the control central to silence it? If you did it should work. I would suggest you reset your Watch. Press the crown and side button in until the Apple logo appears. Then see how you get on.