This worked for me as well. I know this is an old thread but still relevant.
hi. i have just purchased this and can get all notifications apart from text messages. ive tried everything mentioned on this page. can anyone help?
Text messages have another level of control which is dependent on your phone's settings. Ensure you have ticked all the notification boxes you want in Garmin Connect. Then open your 'messages' as if you were about to check who had sent you texts. Click on the three dots on top right. Click on settings. Next click on notifications. You will see that a line saying 'incoming messages' will have been ticked. Click on that line and hold it for a few seconds. Advanced settings will then appear, giving you options under the title 'behaviour' with the option to receive notifications by sound or by display - or both. Tick both. Ensure that 'show notifications' is also ticked as it already should be. This worked for me after a lot of searching.