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I Googled around about the state taxes. Taxact has a page with all the states listed with what they know: https://www.taxact.com/support/[social security number removed]/american-rescue-plan-unemployment-ex... 

For NY it says the following:

"New York does not currently conform to the federal exclusion, but has not released guidance on adding back the exclusion. The TaxAct New York program currently allows the unemployment exclusion, but you may need to amend your return if the state decides not to conform."