Doh! It’s embarassing, but I’ll leave this here in case anyone else runs into the same problem.
After writing the message above, I looked yet again at the path in Tools | Configuration and found this:
/home//mydomain/public_html/
(I’ve ordered my new computer glasses but they haven’t come yet

)
I still don’t understand how the double slash allowed File Manager to access the root (public_html) but cut off the first letter of the subdirecteries below that or why the error is "Access denied."
Bob