### 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 extension_list_config_file = GDExtension::get_extension_list_config_file();
	if (FileAccess::exists(extension_list_config_file)) {
		files.push_back(extension_list_config_file);
	}
	
	if (TS->has_feature(TextServer::FEATURE_USE_SUPPORT_DATA)) {
		bool use_data = GLOBAL_GET("internationalization/locale/include_text_server_data");
		if (use_data) {
			
			if (!TS->get_support_data_filename().is_empty()) {
				String ts_data = "res://" + TS->get_support_data_filename();
				if (FileAccess::exists(ts_data)) {
					files.push_back(ts_data);
				} else {
					
					String abs_path = ProjectSettings::get_singleton()->globalize_path(ts_data);
					ERR_FAIL_COND_V(!TS->save_support_data(abs_path), files);
					if (FileAccess::exists(abs_path)) {
						files.push_back(ts_data);
						
						MessageQueue::get_singleton()->push_callable(callable_mp_static(DirAccess::remove_absolute), abs_path);
					}
				}
			}
		}
	}
	return files;
}
Error EditorExportPlatform::export_project_files(const Ref<EditorExportPreset> &p_preset, bool p_debug, EditorExportSaveFunction p_func, void *p_udata, EditorExportSaveSharedObject p_so_func) {