Here is my 2 cents.  You do NOT add back the estimated PTET payment that was made on 2021 on the partnership return it is deductible and you do not use the accrual method of accounting to adjust it to the actual tax that is computed on the PTET annual return.  It is treated as cash basis and in 2022 you will pick up any overpayment as a refund or bal due as a deduction.

This credit is adjusted as an addback on the 1040 not the partnership return.   I think the credit goes on line 1 47a on page 9 part 2 of the IT-204 BUT there is no code 653 that should be there. TELL pro series to get it together....

My workaround it on the individual K-1, IP p4 answer quest Q and on the Supplemental information I put IT-653 PTET Credit with the amount.  I think that works unless they match but I think NYS will pull the PTET information from the online filing of the PTET return.

Hope this helps and if anyone has a better solution let me know - other that wait out the program fix if they ever do one, they have not for several NYS items such as the Hot Spot deduction.