why wouldn't an accrual based taxpayer deduct from their federal return and add back to the state return the exact amount of the PTET tax, regardless if an estimate is paid or not?    

Cash basis taxpayers should deduct the 2021 estimate if paid from their federal return but add it back on the CT 34-sh (s corp), IT-204-IP (1065).  (The input is there on the 1040 module for this in the K-1 screen).  The credit they claim is the exact amount that is computed on the NYS online services website filing.  

And how are you both deducting for the estimated tax payment on your NY tax return and also passing through the tax credit to the shareholder?  isn't that the classic double dip?