After you changed an "Activity info" to Google Calendar in the watch settings, keep the watch connected and:
(Optionally) You can add more calendars by entering their ids (typically a mail).
To get more calendar ids paste them from Google Calendar settings to watch settings separated by spaces
Change Activity Info to Google Calendar in Garmin mobile Connect app watch face settings.
Get a link and code from your watch
When succeeded, wait for the watch to log-in. It can take 5 minutes or so.
The watch will load your primary Google calendar. You can change which calendars are shown in the watch settings.