Garmin approach s10 doesn't seem to have sync to the Garmin connect app on new phone

A common issue for those that have previously paired with their old phone. BT needs to be completely redone. Follow these steps and video:

• If it exists, remove your Garmin device from the Garmin Connect App (Menu >> Garmin devices).
• "Unpair" all Garmin devices in android Bluetooth settings. Settings >> Bluetooth >> Unpair
• Do the same for any other nearby mobile devices that might have Garmin in its Bluetooth settings. A common issue for users that have a new phone or other mobile devices also paired to the same Garmin device.
• Unpair from the app - Settings >> Apps >> Show System Apps >> Bluetooth >> Storage >> Clear Data
• Reboot your phone, restart your Garmin.
• On your Garmin device place into "pairing mode." Differs per device, but usually in Settings > Phone > Pair Phone to manually enter pairing mode.
• Pair using Garmin Connect Mobile app

If still problems after this, see the more extensive list of possibilities here: Sync / Connection Troubleshooting Guide

And/or contact Garmin Support - https://support.garmin.com

Update: If your phone is running Android 12, when trying to pair your watch, the Garmin Connect Mobile APP says the device is not found until you grant the permission of "Nearby devices." This permission was newly introduced in Android 12 by Google and the permission must be granted for pairing all Garmin devices to the Android Connect Mobile APP.