Here is the state form you can fill in manually : https://www.tax.ny.gov/pit/ads/efile_addit558-2d.htm
Otherwise you will need to download the 2021 program to complete any portion of a prior year return.
See this TurboTax support FAQ for completing a tax return originally started with the online editions - https://ttlc.intuit.com/turbotax-support/en-us/help-article/printers-printing/finish-prior-year-retu...
If you paid for the TurboTax 2021 online edition with a credit card you will need to contact TurboTax support so they can push a 2021 installation file to your download account.
See this TurboTax support FAQ for contacting support - https://ttlc.intuit.com/community/using-turbotax/help/what-is-the-turbotax-phone-number/00/25632
Or download the amendment program ...
https://ttlc.intuit.com/community/amending/help/how-to-amend-change-or-correct-a-return-you-already-...
