Investigate how to close FMU Settings when user close the browser tab

Currently if users close the FMU settings tab, the application will still run. It would be a better UX to shutdown the app when the browser tab is close. One possible solution could be that GUI listen to this close browser event and send shutdown request to API, or maybe the CLI can listen to the browser it opened, if it's closed then shutdown the app.

Start by tracing the CLI, GUI, and API interaction involved when the browser tab is opened and closed. Compare the possible browser-close notification and CLI-supervision approaches, then define and verify one shutdown path that stops the application after the settings tab closes.

Written by the indexing model from the issue text.