No if you have you watch on the watch will be what alerts you. Not the phone. Even if sound is on all the way up on the phone but your watch is connected you’ll feel the watch but your phone won’t ring
this post was submitted on 25 Nov 2023
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Silent mode Graphic highlights general navigation within watchos10 Control center - bell icon
This link has a bit more information
Open Watch app.
Click Notifications > Messages
Make sure Custom is selected and not 'Mirror my iphone'
You can then select deselect sound and haptics.