TurboTax does not file anything for you. It is up to the user to either e-file or mail the returns. Did you e-file and was the state return rejected?
When you e-file your return you will get two emails from TurboTax. The first one will say your return has been transmitted; the second one will tell you the IRS has accepted or rejected your federal e-file. If you filed a state return, there will be a third email (usually a day or two later) that tells you if the state e-file was accepted or rejected.
It is now too late to e-file a 2023 return. The only way to file a 2023 return is by mail. If you prepared a 2023 state return, you will need to print it, sign and date it in ink, and mail it to DC.