> What happens in a court case when this occurs? Does the receiving party get to review and use the redacted information (assuming it’s not gagged by other means) or do they have to immediately report the error and clean room it?
Typically, two copies of a redacted document are submitted via ECF. One is an unredacted but sealed copy that is visible to the judge and all parties to the case. The other is a redacted copy that is visible to the general public.
So, to answer what I believe to be your question: the opposing party in a case would typically have an unredacted copy regardless of whether information is leaked to the general public via improper redaction, so the issue you raise is moot.
"We have documented cases of humans leading normal lives with little to no brain beyond a cerebellum" -- I take this to mean that these are humans that have a cerebellum but not much else.
Your npr.org link talks about the opposite -- regular brain, but no cerebellum.
Your irishtimes.com link talks about cerebrum, which is not the same as cerebellum.
Your biology.stackexchange.com link talks about Cerebral Cortex, which is also not the same as cerebellum.
And the cbc.ca link does not contain the string "cere" on the page.