So, here's the link to the download from the FAQ you mentioned:
https://patchdelivery.turbotax.intuit.com/statecleanup/TY21_StateClean_Tool.zip
See the problem? Yes, the FAQ says it was updated January 2023, but the download has not been updated for 2022.
The good news is I finally got my state tax to work - using H&R Block's software. I'm done with TT, full refund request submitted.
