As you have rightly mentioned, the new tab will also come with the sandbox environment properties, and some of the features will be restricted, similar to the app.
We do not have the flexibility to add these sandbox properties to the app by yourself or on our end.
I will record it as a feature request to add this feature to add this header to your app yourself or on-demand at our end. We cannot share any estimated timeline until the feature is picked up, worked on, and released.