The “Include in app” toggle in Power BI is greyed out on all Power BI workspaces for all service accounts.
Microsoft released an update to Power BI that controls inclusion in Apps from the main screen.
Click on Update App to get into the Update App configuration screen.
Click on step "2. Content" and then "Add content" and add the new report to the Content list below.
Then click on step "3. Audience" and make sure the newly added report is not hidden (it seems to be marked as hidden by default).
Then you publish the app and the new report will now appear in the App.