LBTimer/Shastimer requests the user's permission to access its own data in the user's Google Drive™. The permission is requested using Google's OAuth2 authentication system. The data is stored in a hidden folder accessible only to LBTimer/Shastimer app. The data is accessed using Google's Drive API. You can read more about this hidden folder here.
For the e-mail notification feature, as well as for the functionality of directly sending an e-mail to the developer from the extension panel, LBTimer/Shastimer requests the user's permission to send an e-mail in their name from their Gmail account. E-mails are sent using Google's Gmail API. If those features are not used, the permission is not even requested.
You can review Google's privacy policies here.
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