### 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)

pkg_name = String(ProjectSettings::get_singleton()->get("application/config/name"));
	} else {
		pkg_name = "Unnamed";
	}
	pkg_name = OS::get_singleton()->get_safe_dir_name(pkg_name);
	
	String path = p_path;
	String tmp_dir_path = EditorPaths::get_singleton()->get_cache_dir().path_join(pkg_name);
	Ref<DirAccess> tmp_app_dir = DirAccess::create_for_path(tmp_dir_path);
	if (export_as_zip) {
		if (tmp_app_dir.is_null()) {
			return ERR_CANT_CREATE;
		}
		if (DirAccess::exists(tmp_dir_path)) {
			if (tmp_app_dir->change_dir(tmp_dir_path) == OK) {
				tmp_app_dir->erase_contents_recursive();
			}
		}
		tmp_app_dir->make_dir_recursive(tmp_dir_path);
		path = tmp_dir_path.path_join(p_path.get_file().get_basename() + ".exe");
	}
	
	String pck_path = path;
	if (embedded) {
		pck_path = pck_path.get_basename() + ".tmp";
	}
	Error err = EditorExportPlatformPC::export_project(p_preset, p_debug, pck_path, p_flags);
	if (p_preset->get("codesign/enable") && err == OK) {
		_code_sign(p_preset, pck_path);
		String wrapper_path = p_path.get_basename() + ".console.exe";