While the Garmin Connect app is in the foreground (shown on the screen) it works but not when it is in the background.
I got it working by enabling
"Display pop-up windows while running in the background…
With thanks to @lgroth! I have a Pixel XL with settings navigation slightly different:
Settings | Apps & Notifcations | See all xxx apps | Connect | Advanced | Display over other apps | Display over…
While the Garmin Connect app is in the foreground (shown on the screen) it works but not when it is in the background.
I got it working by enabling
"Display pop-up windows while running in the background"
"Display pop-up window".
"Show on lock screen"
These settings are found in the Settings application here
Apps -> Manage apps -> Connect -> Other permissions
My device is a Xiaomi Note 10 Pro running Android 9.