When should we expect IRS to correct 2020 filing based on $10,200 reduced income provision?

They are starting to go out. See this new IRS article May 14, 2021
https://www.irs.gov/newsroom/irs-begins-correcting-tax-returns-for-unemployment-compensation-income-exclusion-periodic-payments-to-be-made-may-through-summer

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