I want to know if my extension went through

The IRS says that if they do not tell you that your extension was rejected, you can presume that your request for an extension was accepted.

If you got an email from TurboTax confirming the extension, keep it because that's your proof.

I received a notice from Turbotax that my payment went through but nothing on my extension. How do I know that my extension went through.

There is no actual confirmation from the IRS for an extension, but you should get an email from TurboTax that tells you it was sent.  Be sure to check your spam/junk emails if you don't see it.