There is no 'Add Device' option on the Windows version of Garmin connect.
I'm logged into https://connect.garmin.com/modern/. If I click the small watch in the top right corner I see my Vivoactive 3 watch, but not my S2.
My watch is connected to the PC via USB and I can see it when I launch Garmin Express, but I don't see it on Garmin connect.