Hello @Michael Schmidt
You are right, after creating" the AppService, the SKU(App Service Plan) and the App Service have to stay "up and running" to be able to receive HTTP requests.
App Service Plans that have AppService or does not have AppService associated with them still incur charges because they continue to reserve the configured VM instances.
https://learn.microsoft.com/en-us/azure/app-service/app-service-plan-manage#delete-an-app-service-plan
So Microsoft will still charge you after you stop the AppService.