We didn't realize the deadline had been extended so we filed an extension electronically. We mailed a paper return on 4/20/2021. 'Where's my refund' shows nothing. ??

Given the backlog at the IRS it is not surprising that you are not seeing anything about your mailed return yet.

MAILED RETURNS

Per the IRS:

COVID-19 Mail Processing Delays

It’s taking us longer to process mailed documents including:

• Paper tax returns, and
• All tax return related correspondence.

We are processing all mail in the order we received it.

Do not file a second tax return or call the IRS.

 It can take 3-4 weeks  (or a LOT longer since the IRS is severely backlogged) for anything to show up on the IRS site when you mail a tax return.  Expect at least 6-8 weeks for complete processing of a mailed return and probably  MUCH MUCH longer.

If  you mail a tax return (or a payment) to the IRS, it is a good idea to use a mailing service that will track it like UPS or certified mail so you will know it was received.

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. 

TurboTax will not know anything about your mailed return, and will continue to show “Ready to Mail” on your account.  TurboTax will not know that you put your tax return in an envelope and took it to a mailbox.  TurboTax does not get updates on mailed  (or e-filed) returns.

When the IRS opens its mail and begins to process mailed returns you can check the status on the IRS site. https://www.irs.gov/refunds

State returns have to be mailed to the state.

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

If you are wondering if you should send your return again——the IRS does not want you to file a second time.   Putting two tax returns into the system at the same time can lead to confusion and even more delays.   If you did not use tracking and do not know if the return was received—-you have to make your own judgement call and decide if you want to risk further delay by sending the return again.