Since you permanently moved to FL you are now a FL resident. You will need to file a NY non-resident form to report the NY unemployment. NY does tax non-residents on unemployment benefits earned from NY employment.
In the "My Info" section scroll down to the "Other State Income" topic. There you will select "Yes" you earned money in another state and select NY from the dropdown list. This will generate the NY non-resident return. When you go through the NY state interview you will have the opportunity to allocate only the NY unemployment to NY.
Be advised, NY does use all income to calculate the NY tax on only the NY allocated income. So you will see all your income represented but the tax will only be on the NY portion in the end.
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