How do I get a receipt for the state return e-file?

A receipt from TurboTax would have been sent to your email address.  Your credit card statement will also have the payment posted with the payee being Intuit TurboTax

I did not get an email receipt. Is there a delay in those being sent?

You may also view your receipt/payment information in your TurboTax account. Log into your TurboTax account. On the summary screen, scroll down and under the applicable tax year, click on View order details. From there, you will see the information regarding payment of your TurboTax software.