Should I still amend my federal taxes due to the unemployment tax break?

No, you do not need to amend your tax return for the unemployment compensation exclusion.

The IRS is calculating tax refunds for all those eligible for the exclusion.   They started sending out tax refunds in May and will continue throughout the summer months.

Go to this IRS website for information - https://www.irs.gov/newsroom/irs-sending-more-than-2-point-8-million-refunds-to-those-who-already-paid-taxes-on-2020-unemployment-compensation

No. at this point the IRS does not want amended returns filed for UC exemption.  however, if you now qualify for EIC or CTC that was never claimed on the original, you can file an amended return to claim them once the IRS gets through processing the UC.  be sure to include form 8812.

for your state - some do require amended returns

https://ttlc.intuit.com/community/state-taxes/help/do-i-need-to-amend-my-state-return/01/2134732