If you get notifications on your phone that you don’t want to see on your watch, you can stop specific apps from showing up on your watch. You can edit your notification preferences in the Wear OS by Google app. Tap Notifications under the Settings menu on the main screen. In the Notifications menu, you can toggle off any apps you don’t want to receive notifications for on your watch.
When you listen to music on your phone, you’ll always see the music card with options to pause and play. You can’t turn this card off.