Setting up a new watch: 2 issues

To rule out a software issue inside your backup data, erase the watch and pair it again, setting it up as a new device. You will only lose your created Watch faces and may have to activate the cards in your Wallet app again.

Then test the notifications and sound again.

Unpair and erase your Apple Watch - Apple Support

Did you try to force restart by pressing and holding the Digital Crown and the Side button together for about 10sec, until the Apple logo comes back again?