Try running /Applications/Duplicati.app/Contents/MacOS/duplicati-server from the terminal then browse to 127.0.0.1:8200 to see if it is running.
If that works then add the plist file from my “Edit 2” above so that it runs automatically after reboot.
The update has removed python 2.7 in 13.2 so the menu bar tray icon doesn’t work but the core Duplicati service doesn’t appear to be affected.