For tax year 2020, unemployment was not taxable. However, that tax break did not extend to this year so far. So, this year, you will need to enter your 1099 G from unemployment when you are filing your taxes.
It sounds like you misunderstood last year. Some people filed tax returns with federal tax paid on unemployment before the tax law changed for waiving some of the tax on unemployment. Those people were advised to wait---not amend--because the IRS would adjust their refunds.
Your return had a different issue altogether. You neglected to enter your unemployment on your 2020 return. You do need to amend and enter that 1099G on your amended 2020 return. The software will treat the amount withheld from your unemployment according to the 2020 tax law.
Select your tax year for amending instructions: