The problem has been resolved, and I'm remiss in not reporting the solution. My bad! If you search around, you will find a separate TurboTax support section devoted to state problems with an 800 number. I contacted them, and the final solution (after trying several things) was for me to uninstall the software, then the agent created a dummy invoice for me at $0 and downloaded an entirely new copy of the software, including New York State. Installed that and it worked fine. Both my federal and NY State have been accepted. Total time on the phone - about 90 minutes.
I'm really disappointed in TurboTax! This state looping issue has been around for years, and their July 2021 solution for TY 2020 does not work for TY2921. I doubt I will continue as a TurboTax client, though I've been using them for about 10 years!
