On the vivoactive 3 music, the serial number is on the back of the watch body next to the QR code. This is different to the unit ID. The serial number will be between 8-9 characters or numbers, whereas the unit ID is a 10 digit number. Hope this helps.
This is the right answer as per information on garmin pages.
However, I don't see the QR code and the 8-9 character serial number on the backside of my vivoactive 3 music. It's a pity as the case of my watch is suddenly broken where the belt pins are connected. This seems to be the weak point of this watch.
However, I'm unable to locate the SN and thus claim warranty by Garmin :-(
Go to https://connect.garmin.com/modern/ login and select the device icon in the top right corner. Click on ' device settings' and you will see the serial number there. You can also get there through express and clicking ' Garmin Connect'