The issue seems to be the .toolbarBackground modifier, not the Map itself. I see the same problem when using a MKMapView, as long as I add that modifier. However, as you correctly described, Map will underlap the navigation bar by default and thus requires the .toolbarBackground modifier to achieve the desired look. Sadly I couldn't yet find a solution for customizing the back button appearance (which, to my knowledge, isn't possible without resorting to UIKit and appearance proxies) while using .toolbarBackground. Any pointers are much appreciated!

Did you try this method? Using the above, I was able to customize the filename for all exports. However, I didn’t manage to set a filename that depends on the item I’m exporting. But maybe it solves your specific problem.