If I received a refund check I wasn't expecting, what should I do? How do I find out if it's an error or a legitimate correction?

Did you file a 2020 tax return that had unemployment BEFORE the tax law changed?   Or was your stimulus payment based on 2018 or 2019 instead of  a lower  2020 income?  You may have just received the "extra" refund for unemployment you paid tax on, or a "plus up" stimulus payment.

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

https://www.irs.gov/newsroom/irs-treasury-disburse-more-economic-impact-payments-under-the-american-rescue-plan-total-tops-130-million-with-more-to-come

You will get a letter explaining the refund. It might be a few weeks before you get the letter. When you see what the letter says you'll be able to figure out whether the refund is correct or an error.