Pitfalls of Syncing Google with Google

Take caution not to use the app to sync Google with itself, as that won't accomplish anything.  Instead, consider syncing your Google account with one of your Apple accounts, such as iCloud.

See this article for more info on how to select an account to sync with Google:
https://playaapps.zendesk.com/hc/en-us/articles/226468868-How-To-Select-2-Accounts-to-Sync