If you filed a federal form 4868 extension request a copy of the form 4868 was supposed be included with the Georgia state tax return meaning the Georgia tax return needed to be mailed. Since you e-filed the tax return mailing a copy to the Georgia DOR may not be needed if you did not have any Georgia state taxes owed on the 2021 tax return you filed or the state return has a state tax refund.
If taxes were owed on the 2021 Georgia state tax return, then you need to speak with a Georgia DOR agent for how to submit the Form 4868 so that you can at least avoid the failure to file penalty.
Go to this Georgia DOR website for a phone number and/or how to send an email - https://dor.georgia.gov/help/contact-us
