When you stop the App Service you will notice that it still billing you even after it is shutdown! also if you go to the app service over view you will notice a message saying “Your App is stopped. App Service Plan charges still Apply.”
I know it is weird but when your app service plan is under anything other than the free tier you will notice this.
So there is only one way to stop the billing completely by moving you app service to a Free tier.
In-order to do this go to the Scale up (App Service Plan) on the App service and scroll down to the bottom and select the F1 Free tier to apply the change.
Once the plan is updated you can go under the App Service plan from the App service and check the latest pricing tier.
So when the app is completely stopped you will see the app service as below.