Hi @Dan Morgan
That second icon is New Outlook’s system-tray icon, not another copy of Outlook. The “trace” options are diagnostic tools used to collect performance or network logs when troubleshooting Outlook, which is why they do not contain normal mail commands.
Closing the icon also closes Outlook because it represents the running application. If you only want to hide it, open Windows Settings > Personalization > Taskbar > Other system tray icons, then turn off Outlook. It may still appear under the hidden-icons arrow while Outlook is running.
Hope my answer helps. Have a nice day!