In general, when users attempt to access a private Experience Builder app on ArcGIS Online, they are directed to the main ArcGIS Online sign-in page. To send users to your organization's sign-in page instead, use org followed by your organization's short name.
https://experience.arcgis.com/experience/<AppId>/?org=<yourorgshortname>
--from https://doc.arcgis.com/en/experience-builder/latest/build-apps/url-parameters.htm
@DanMallett did you try the URL in this format: https://experience.arcgis.com/experience/<AppId>/?org=<yourorgshortname>
This way does work for me. Could you share your URL to me so we can have a try.
Thanks,
Wei