The tax return on file with turbotax has no reference on the return that it was signed or submitted electronically. Where is the verification that is was signed?

Did you efile?  Was it Accepted?  There is no actual signature on a efiled return.   You verify it by entering the last year’s AGI.   If you need a copy of the signed return you print it out and sign it in ink at the bottom.   

Did you go all the way through the File tab, through the 3 steps and hit the big orange Transmit Returns Now button?

When you efile you get back 2 emails.  The first email only confirms the transmission.  The second email says if the IRS (or state) Accepted or Rejected your efile.  And check your spam folder for them.

When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc.  What does it say?

How to check the efile status

https://ttlc.intuit.com/turbotax-support/en-us/help-article/electronic-filing/check-e-file-status/L9XhHDPtD_US_en_US

If you efiled, In the PDF of your TurboTax return, the last page of the federal return should be an "electronic postmark" that shows your name, Social Security number, the date and time that you e-filed the return, and the date that the IRS accepted it.