ConnectStats got its first release in a while this week. It now supports notifications. This is currently not enabled by default, you’ll need to enable it explicitly in the services configuration page for Garmin.
The notification only works if your source of activity include Garmin and ConnectStats as a source. It is not possible to get notification into connectstats if you use Strava as a service.
If you enable the feature, you will receive a notification when a new activity is ready, and the app will try to download this in the background. Note that this background update is subject to Apple triggering the app in the background, and it is not guaranteed and consistent. If you got notification but when starting the app the activity is not preloaded, just do a manual update.
To enable this you’ll need to select
New Activities in the Notification setting for garmin as below.