If you use the LaunchDaemon plist I posted in the other thread (“how to run with root privileges on a Mac”) to run the Duplicati server, you would get logging in /Library/Logs. Changing the log level can be done in the plist in the --log-level parameter.
And he is correct that --log-level can be used to specific the detail of the text log that is written to when using --log-file (without which most log info is written to the .sqlite database files).