Turbo tax appears to be transmitting federal return, but Check E-file status indicates it has not been filed.

Did you e-file your tax return and was it accepted?  

You complete your tax return by finishing all 3 Steps in the File section.  In Step 3, to e-file your tax return, you must click on the large Orange button labeled "Transmit my returns now".  

After completing the File section and e-filing your tax return you will receive two emails from TurboTax.  The first email when your tax return was transmitted and the second email when the tax return has either been accepted or rejected.

Use this TurboTax website to check the status of an e-filed return and if it was either accepted or rejected -https://turbotax.intuit.com/tax-tools/efile-status-lookup/

If accepted by the IRS use the federal tax refund website to check the refund status -  https://www.irs.gov/refunds

If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

·         Per DoninGA

Submission only takes a few minutes at most. Then you wait for ACCEPTED, or REJECTED.

If you are stuck on Submitting, you need to restart, re-login, or re-boot.

I'm looking for my refund?

I'm looking for my 

I'm looking for my refund

I have exactly the same issue with my 2020 federal taxes, using TT Deluxe desktop edition. Was there a solution on this one?

If your return is not transmitting properly, please click here to contact customer support @nikolab.

I received two emails after the transmition, one saying that it was accepted, and one saying that it was approved. I guess that is a sign that it was transmitted OK. Am i right?

Yes. You can also check your status when you click here @nikolab.