As you pointed out, the issue is not specific to - and therefore cannot be fixed in - /e/OS. It seems to be a problem with any custom ROM using microG in place of Google Play Services. So the fix is either going to come from microG or from Garmin Connect.
I made it easier by creating a launcher shortcut to the file and positioning the shortcut next to the Garmin Connect icon in my launcher homescreen. I can open the app just be clicking on the shortcut. (Note that I use a proper launcher - Lawnchair Legacy from Aurora Store - not the broken /e/OS launcher )