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I am looking into this one, which fortunately I am still able to replicate on the older machine I mentioned earlier. Something is messed up with the XDG desktop paths; on my system "kde-config --userpath desktop" returns "/".
Confirmed here.
On my virtual machine running Trinity I get "/" for both root and normal user.
On my 3.5.10 machine I get the correct location for the Desktop directory for both root and normal user.
That probably confirms why the original desktop icons are missing.
That bug probably exlains why a new .directory files is being created in the root level of the files system when I run as root, and why I receive the error message trying to create that same file when running as normal user.