Integrations now has Calendars added to Google Calendar, which lists Personal and each team you belong to. For each one, choose Not added or All events. Teams also offer Only events I'm going to, which covers events you answered Going to and events you created. Personal starts as All events; teams start as Not added, so nothing from a team reaches your Google Calendar until you choose it.
Events from the calendars you choose, including upcoming ones that already exist, are added to your own Google Calendar within about a minute. Changes and deletions in Magpie follow. Choosing Not added, leaving a team, or a team being archived removes that calendar's upcoming events from Google Calendar.
Each copy follows what Magpie shows you: a team event you can see only as busy is added as "Busy", and a title-only event is added without its description or location. Copies send no invitations. Personal events now also reach Google Calendar within about a minute rather than immediately.