When you authorize your Google calendar in Sprout Studio, you are not adding your Sprout Studio calendar to Google. Instead, you are authorizing Sprout Studio to view your Google calendar. Some users mistake this step for adding their Sprout Studio calendar into Google.
As explained in this article, there are two ways to integrate your calendar with Sprout:
Incoming, which allows Sprout to read your existing external calendar.
Outgoing, which allows you to see your Sprout calendar on your existing calendar.
Authorizing your calendar in your Profile modal is the first step - setting up the incoming calendar. To view your Sprout Studio calendar in your Google account or Apple calendar, you must add the outgoing calendar, which is the second step.
Follow the instructions here to view your Sprout Studio calendar outside of Sprout Studio.