If you have filed. The IRS will recalculate your return for the new 10,200 unemployment exemption for you. 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.

See new IRS article May 14, 2021

https://www.irs.gov/newsroom/irs-begins-correcting-tax-returns-for-unemployment-compensation-income-...

Do you need to amend your state return?

https://ttlc.intuit.com/community/state-taxes/help/do-i-need-to-amend-my-state-return/00/2134732

What’s the estimated time to receive the payment. 

Sometime starting in May and continuing over the summer.