Do I need to take any action to get my additional refund for the unemployment taxes that were withheld in 2020? I filed prior to the announcement that it would be nontax.

No, there is nothing for you to do.  The IRS will be calculating and issuing the tax refunds based on the unemployment compensation exclusion for all who are eligible.

Go to this IRS website for information - https://www.irs.gov/newsroom/irs-begins-correcting-tax-returns-for-unemployment-compensation-income-exclusion-periodic-payments-to-be-made-may-through-summer

And this IRS website for exclusion FAQ's - https://www.irs.gov/newsroom/2020-unemployment-compensation-exclusion-faqs

Your unemployment is not necessarily all nontaxable, and you won't necessarily get a refund of all the tax that was withheld. The first $10,200 of your unemployment is nontaxable. The IRS will exclude up to $10,200 of unemployment from your income, and recalculate your tax return accordingly.