When I set up the watch I did not get notifications from the phone until I (in the wearable phone app) activated the global switch in the notification settings for "All Apps". (This is at the top of the list with all apps where you enable notifications for individual apps.) After that I could go through the list and clear those I didn't want. (I have replaced and installed 3 different watches to my phone and this step was needed every time.) Give it a try ...
Same issue. It turns out that do not disturb mode on my phone got turned on somehow. It would still allow the notices to come through to the watch but was overriding all of the sound options on the watch. Hope that helps.
I did run through the usual troubleshooting steps first:
1) restart watch
2) restart phone
3) make sure apps are up to date
4) reinstall Samsung apps on phone
5) factory reset Galaxy Watch