You do not need to amend your return for unemployment the IRS will make the adjustment. 

"If you have already filed your 2020 Form 1040 or 1040-SR, there is no need to file an amended return (Form 1040-X) to figure the amount of unemployment compensation to exclude. The IRS will refigure your taxes using the excluded unemployment compensation amount and adjust your account accordingly. The IRS will send any refund amount directly to you. "(IRS)

Please see IRS to recalculate taxes on unemployment benefits; refunds to start in May for additional information.

I believe CNBC posted that you DO need to file an amendment if you have Obamacare or other issues that are income dependent and may give you more back than the simple calculation the IRS will do. I am not sure why the IRS would not also figure that out. But that is what I read. I guess stay tuned, nothing finalized yet.

Yes, according to this IRS website "there is no need for taxpayers to file an amended return unless the calculations make the taxpayer newly eligible for additional federal credits and deductions not already included on the original tax return."