### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

bool use_storyboard = p_preset->get("storyboard/use_launch_screen_storyboard");
		String launch_image_path = dest_dir + binary_name + "/Images.xcassets/LaunchImage.launchimage/";
		String splash_image_path = dest_dir + binary_name + "/Images.xcassets/SplashImage.imageset/";
		Ref<DirAccess> launch_screen_da = DirAccess::create(DirAccess::ACCESS_FILESYSTEM);
		if (launch_screen_da.is_null()) {
			return ERR_CANT_CREATE;
		}
		if (use_storyboard) {
			print_line("Using Launch Storyboard");
			if (launch_screen_da->change_dir(launch_image_path) == OK) {
				launch_screen_da->erase_contents_recursive();
				launch_screen_da->remove(launch_image_path);
			}
			err = _export_loading_screen_file(p_preset, splash_image_path);
		} else {
			print_line("Using Launch Images");
			const String launch_screen_path = dest_dir + binary_name + "/Launch Screen.storyboard";
			launch_screen_da->remove(launch_screen_path);
			if (launch_screen_da->change_dir(splash_image_path) == OK) {
				launch_screen_da->erase_contents_recursive();
				launch_screen_da->remove(splash_image_path);
			}
			err = _export_loading_screen_images(p_preset, launch_image_path);
		}
	}
	if (err) {
		return err;
	}
	print_line("Exporting additional assets");
	_export_additional_assets(dest_dir + binary_name, libraries, assets);