### 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)

String base_file = p_path.get_file().get_basename() + ".scn"; 
			save_path = export_base_path.path_join("export-" + p_path.md5_text() + "-" + base_file);
			Ref<PackedScene> s;
			s.instantiate();
			s->pack(node);
			Error err = ResourceSaver::save(s, save_path);
			ERR_FAIL_COND_V_MSG(err != OK, p_path, "Unable to save export scene file to: " + save_path);
		}
	} else {
		Ref<Resource> res = ResourceLoader::load(p_path, "", ResourceFormatLoader::CACHE_MODE_IGNORE);
		ERR_FAIL_COND_V(res.is_null(), p_path);
		if (!customize_resources_plugins.is_empty()) {
			for (Ref<EditorExportPlugin> &plugin : customize_resources_plugins) {
				Ref<Resource> new_res = plugin->_customize_resource(res, p_path);
				if (new_res.is_valid()) {
					modified = true;
					if (new_res != res) {
						res = new_res;
					}
					break;
				}
			}
			if (_export_customize_object(res.ptr(), customize_resources_plugins)) {
				modified = true;
			}
		}
		if (modified || p_force_save) {
			
			String base_file = p_path.get_file().get_basename() + ".res";