My try of Computer/Share/Folder (without any leading slash) on 2.0.3.9 put “Test connection” work in the current directory of Duplicati.Server.exe which is C:\Program Files\Duplicati 2 (per Process Explorer) but possibly varies. Duplicati updates run from the update directory, so maybe the current directory is there.
For the UNC path problem, I’m seeing few forum complaints, however there was some discussion in topic Service Install Backup to UNC Paths. My own attempt ran into some problems, but it’s to an old share in a somewhat unknown condition, so I’m not willing to blame Duplicati too quickly. Could you say your result?
EDIT: or maybe you did in the second post, however that’s not a UNC path either? The forum software can sometimes eat a backslash (perhaps to quote the next character, as UNIX shells do), but I see none at all. This makes me notice that when I quoted your original post with two backslashes, it showed as an asterisk and a backslash. I just made that three backslashes, and at least the preview is showing two, as I desired.