OK, that is useful information. It might be something Pi Zero specific, I don’t think I have had any success or failure feedback on it from other users.
If you log into dietpi, and stop the service:
systemctl stop roon-extension-manager
Then switch to the Extension Manager directory:
cd .RoonExtensions/lib/node_modules/roon-extension-manager
And run it from the command line:
node .
Does it keep on running, what output do you get on the console, any errors?