I filed an extension and paid my taxes in April, but not through TurboTax. How do I file my taxes through TurboTax without having to re-pay my taxes owed?

Have you filed yet?  If not you can enter it.  

For 2021 Federal Extension payments should be on schedule 3 line 10. And go to 1040 line 31.

You can type estimates paid in the search box at the top of your return and click Find and it will give you a link to Jump To the screen where you enter Extension Payments.

To enter the amount you paid with an extension (including state extension) go to

Federal Taxes (or Personal for desktop H&B version)

Deductions and Credits

Then scroll way down to Estimates and Other Taxes Paid

Other Income Taxes - Click the Start or Update button

Next page second section Payments with Extension

Either Visit All or Click Start or Update by the extension you paid