Once Duplicati is running as a service and the trayicon is closed, you will still be able to access the GUI by going directly to http://localhost:8200/ , does that work?
As far as the active service, there is nothing to associate. If the service is running and the TrayIcon icon properties is set to --no-hosted-server you should be connected to the service instance on port 8200.
If the --no-hosted-server is not specified, in the wrong place or otherwise not correct then the TrayIcon will launch a new server instance on port 8300 and connect to it instead.
I’m not sure how you setup Duplicati to run as a service but I found this post by johnvk to be a good set of instructions.