The mystery is solved!
The anomaly is caused by the ESET Internet Security security software, specifically the “Browser Protection” feature. Since version 18.2.14.0, this feature locks the Firefox profile for editing, even when it is closed.
This explains the inability to delete Firefox files. When I included CCleaner in the exceptions of the aforementioned Browser Protection feature and ran the cleanup, everything it has was properly deleted and was not offered for deletion again.
Firefox add-ons now also display correctly in the CCleaner environment.
So for anyone who might have the same problem (maybe with a different browser).