If I filed for an extension for my 2023 taxes, paid $6000 with the extension, but didn't finish filing, do I put down that I didn't file my 2023 taxes ?

Are you trying to enter a 2023 AGI to e-file 2024?   Say that you did not file 2023, or try using zero as your AGI to e-file.

Meanwhile----why have you not finished 2023 and filed it?

 You will be able to access the 2023 return you started by using the exact same account and user ID that you used when you started it.   But you can no longer use online software for any further changes.

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 

Start a 2024  return online and enter some personal information  so that the menu on the left opens up and lets you access your past year returns.

Online tax preparation and e-filing for 2023 returns is now permanently closed.

Now it is too late to use online software or to e-file. If you have any changes/corrections at all to make to your 2023 return, you now have to complete it using desktop software, which you must download to a full PC or Mac  (not to a mobile device).Then you need to print, sign and mail it.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/printers-printing/finish-prior-year-return-started-turbotax-online/L9Oe4M90A_US_en_US?uid=m68tffpe

If you already paid for your online software you can ask customer support for a download of the desktop software.

They are available from 5 a.m. to 9p.m. Pacific time daily

https://ttlc.intuit.com/questions/1899263-what-is-the-turbotax-phone-number

If you are getting a refund, there is no penalty for filing late.  If you owe tax due, then file and pay the amount due as shown on the Form 1040, but expect a bill later from the IRS for the penalty and interest you will owe.  Only the IRS will calculate this—TurboTax will not calculate it.

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.  Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.

Federal and state returns must be in separate envelopes and they are mailed to different addresses.  Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.