That shouldn’t matter. The key part here is Row IDs. Glide Tables have Row IDs inheritently built in. You can add a Row ID column, but I don’t think it’s required. As for other data sources, such as Google Sheets, you have to explicitly add a Row ID column. Then the urls should work.
Is there any differences between your main app and your dummy app, such as different data sources, or Row ID in one, but not the other? I have Public, Public with Email, and Private apps that all give me specific urls for the screen, but you have to make sure it has a Row ID because that is a big part of how the url is formulated.
I will add though that in one of my old apps, I don’t get special urls at the tab level. I think my app is still running on an old computation model. However, if I navigate to the details of a list item, I still get the special url. Maybe that’s one difference between your main app and dummy app. I think you can tell which computation model the app is using by looking at the privacy settings. The privacy settings screen has an updated look on newer apps compared to older apps.
But, either way you should have the special urls to some degree regardless of your privacy settings.