You should only have to amend your 2019 federal return if you itemized deductions last year. You can go through the amendment steps and see if there is an impact on your NJ return. If there is any tax owed to NJ after you enter the 1099-G then print and mail the amended 2019 NJ return.
However, it's only taxable to the extent that it's more than the refund you would have received by choosing the larger refund from these: Standard deduction. General sales tax.
