Unless you have a New York state tax return, then you will have to pay the e-file fee for a state return using the desktop editions of TurboTax. Or you can print and mail the state return to avoid the fee.
Or you can use the TurboTax online editions which do not have an e-file fee but charges a fee for the state program software
TurboTax has charged an e-file fee for a state return using the desktop editions for decades, this is not new.
You can file federal and state using the Free Edition if you have a VERY simple return. If you need a paid version for the federal return you will also have to pay for the state return. Or....if you use the CD/download you can purchase versions of the CD/download that include state software.
However, if you use the CD/download, even if the software has the state program to prepare a state return, there is always--always---an extra fee to e-file the state. You can avoid the e-file fee if you print and mail the state.