What is this ~$6,000 amount? Is it the amount of NY state tax that was withheld by your employer?
To file an extension, follow Diane's instructions, and pay at that time whatever you expect to owe to NYS. But if I follow this thread correctly, you don't expect to owe NYS anything, so don't pay them anything when you file for the NYS extension.
If you meant something else (I honestly don't know what "~ $6000 is the amount that was not deducted for the NY state tax in 2021 and which I ideally DO NOT owe. But since Box-15 on the current W2 form says NY - it indicates that I've payed ~ $6000 less state tax in 2021." means), please come back and tell us.
@LilpilJhon
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