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The problem with "too many files were modified" during update was that some incorrectly packed module damaged system files checksums. I've reset files hashed and update worked just fine.
Usually this situation shouldn't happen, but just in case you need to regenerate hashed it can be done by opening the following URLs:
https://example.com/m/developer/reset_hash/system - for system hashes
https://example.com/m/developer/reset_hash/modules - for all modules hashes