Is there a document I can print in order to prove I have been approved for my extension request? All I received was an email.

The IRS does not issue any type of confirmation that an extension request was approved.

The email you received from TurboTax should show that the request was accepted with the date of being accepted.  Since the IRS accepted the Form 4868 it has been approved.

See this TurboTax support FAQ for printing the Form 4868 extension request - https://ttlc.intuit.com/community/printing/help/how-do-i-print-my-4868-extension-form-after-e-filing-it-through-turbotax-easy-extension/01/26520

just the email.  the IRS (nor do states) does not confirm that an extension were successfully filed.   and approval can depend on the accuracy of the extension request - a substantially underestimated tax liability could invalidate the request.   the IRS can't determine this until the actual return is filed.   even if it was unsuccessful, if you are due a refund there will be no penalties.