Must the Project Plan 365 app be open to use Siri Shortcuts on iPhone?
No! Only for the Show Project Status Shortcut to work, a project file should be open. Otherwise, Siri will ask you to either open a project, or if you want the status of the Sample Project to be shown. If you set the Siri Shortcut to show status of a specific project, Siri will show the Project Status of that project even when the app is not running.