Do I need to report my last years tax refund amounts (Federal & State) on this years taxes ?

If you itemized federal deductions for 2021 you will need to enter the state refund you received for 2021.  There is no place to enter the federal refund you received.  It is not taxable.

State Income Tax refunds may be taxable income for federal purposes for individuals who itemized their deductions on their federal tax return in the previous year.  Federal refunds are not taxable and should not be entered on the tax return.

Use this link for more information.