I also installed my smartwatch just for notifications.
To improve provacy, I do not grant any permissions to Google (installation required) and no network permissions to wearos. On setup, I did not connect the watch to the Playstore. Additionally, I deactivated all progs on the smartphone I don't need (such as Playstore, the manufacturer's apps, Fit, Wellness, Google Pay and so on, saving significantly battery power.) Also, in wear os on the phone stopped cloud services.