You only need to file a 2020 NY tax return if you want a refund of the NY tax withheld from this payment.
Since you ended your NY residency in 2019 and were a FL resident for 2020, then you wouldn't need to file a 2020 NY tax return other than to get a refund of NY tax withheld.
There is a possibility that NY will treat the payment as NY-sourced income and want to tax you on the amount paid. The NY state tax interview in TurboTax should help determine whether this will be the case.
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