Hi
The Activity app runs all the time and cannot be stopped. I think you may mean that you started a Workout using the Workout app (the icon for this is a running person on a green background). That would certainly use more battery as the watch measures heart rate continuously during Workouts.
Stopping a Workout
To stop a Workout that is still running:
Go to the apps on your Apple Watch by pressing the Digital Crown once.
Tap on the Workout app.
Either:
- Force press on the display to see Pause / End (and tap on End) or
- Swipe all the way to the left to see Pause / End (and tap on End).
Use the Workout app on Apple Watch - Apple Support
Restarting Apple Watch
After you have checked this, you can also try restarting your Apple Watch, which may help if the problem continues.
Restart: Press and hold the side button until you see the Power Off slider; Drag the slider to turn off completely; Afterwards, press and hold the side button until you see the Apple logo.
Restart your Apple Watch - Apple Support
Tips for maximising battery performance
See also this article: https://www.apple.com/uk/batteries/maximizing-performance/#watch