After you file

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...