What does "You've reached your Google sending limit" mean?
Google has a daily sending limit of 500 notifications a day for Gmail and 2000 a day for Google Apps. This mechanism is at the control of Google's servers and is not something that is controlled by Zendesk. As a proactive measure, to help prevent you from reaching your rate limit for Google, Zendesk will restrict your use at 1500 notifications when you have the Gmail connector enabled, to prevent your Gsuite account from being completely disabled. This setting can be found in your account by going to Admin > Channels > Email > Send email via Gmail.
To avoid this error you can forgo the use of the Gmail connecter and setting up a forwarding rule instead. Please note that by forgoing the use of the connector, you will need to [optionally] set up an SPF record, for you domain to permit Zendesk sending emails on its behalf.
You may find the reason for reaching your Google sending limit by looking at your Gsuite Activity dashboard to see the total amount of emails sent. For more information on this, see Acccount activity reports - Gsuite.
For any discrepancies or inaccuracies, please reach out to Gsuite Support for further guidance on why this limit was reached.