Does TurboTax automatically deduct your estimated taxes from your Extended Federal Return?

Yes if you enter them.   Did you pay in Estimates or a payment with the extension?

To enter Federal or State Estimated Taxes Paid, including a state estimated payment made in January for the prior year, go to

Federal on left or at top.  Personal (Home & Business)

Deductions and Credits at top

Then scroll way down to Estimates and Other Taxes Paid

Estimated Taxes - click the start button

Do not enter them as Other Federal Withholding!  Only enter them in one place.

For 2020 Federal Estimated payments should be on 1040 line 26.

Did you use TT to request the extension?   If so then the estimated payment should have already been entered, but you can check to see if it is there, and enter if it if it is not there yet.

When you requested your extension you were supposed to pay your estimated tax due.  Did you enter the payment you made into your tax return?  Go to Federal>Deductions and Credits>Estimates and Other Taxes Paid>Other Income Taxes 

Hopefully you are already aware that your 2020 return cannot be e-filed now.   It can only be filed by mail.