### 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)

}
	if (!template_path.is_empty() && !FileAccess::exists(template_path)) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Prepare Templates"), vformat(TTR("Template file not found: \"%s\"."), template_path));
		return ERR_FILE_NOT_FOUND;
	}
	
	Vector<SharedObject> shared_objects;
	String pck_path = base_path + ".pck";
	Error error = save_pack(p_preset, p_debug, pck_path, &shared_objects);
	if (error != OK) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Could not write file: \"%s\"."), pck_path));
		return error;
	}
	{
		Ref<DirAccess> da = DirAccess::create(DirAccess::ACCESS_FILESYSTEM);
		for (int i = 0; i < shared_objects.size(); i++) {
			String dst = base_dir.path_join(shared_objects[i].path.get_file());
			error = da->copy(shared_objects[i].path, dst);
			if (error != OK) {
				add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Could not write file: \"%s\"."), shared_objects[i].path.get_file()));
				return error;
			}
		}
	}
	
	error = _extract_template(template_path, base_dir, base_name, pwa);
	if (error) {
		return error;
	}