Unresolvable "Checksum does not match the primary checksum"

This issue was used to investigate a number of issues which are now spun off as "Linked items".

The last remaining undiagnosed problem here is:

Some project repos are persistently failed with last_sync_failure Verification failed with: Checksum does not match the primary checksum. Rechecksumming these project repos on the primary site (as in the workaround for #427493 (closed)) does not resolve the verification errors.

At the moment, there is no known mitigation, nor do we know the cause. The latest discussion is at #426778 (comment 1596109810).