### 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)

#endif 
		Vector<Ref<EditorExportPlugin>> export_plugins = EditorExport::get_singleton()->get_export_plugins();
		for (int i = 0; i < export_plugins.size(); i++) {
			if (export_plugins[i]->supports_platform(Ref<EditorExportPlatform>(this))) {
				PackedStringArray export_plugin_android_libraries = export_plugins[i]->get_android_libraries(Ref<EditorExportPlatform>(this), p_debug);
				for (int k = 0; k < export_plugin_android_libraries.size(); k++) {
					const String resolved_android_library_path = _resolve_export_plugin_android_library_path(export_plugin_android_libraries[k]);
					if (!resolved_android_library_path.is_empty()) {
						android_libraries.push_back(resolved_android_library_path);
					}
				}
				PackedStringArray export_plugin_android_dependencies = export_plugins[i]->get_android_dependencies(Ref<EditorExportPlatform>(this), p_debug);
				android_dependencies.append_array(export_plugin_android_dependencies);
				PackedStringArray export_plugin_android_dependencies_maven_repos = export_plugins[i]->get_android_dependencies_maven_repos(Ref<EditorExportPlatform>(this), p_debug);
				android_dependencies_maven_repos.append_array(export_plugin_android_dependencies_maven_repos);
			}
		}
		bool clean_build_required = _is_clean_build_required(p_preset);
		String combined_android_libraries = String("|").join(android_libraries);
		String combined_android_dependencies = String("|").join(android_dependencies);
		String combined_android_dependencies_maven_repos = String("|").join(android_dependencies_maven_repos);
		List<String> cmdline;
		if (clean_build_required) {
			cmdline.push_back("clean");
		}
		String build_type = p_debug ? "Debug" : "Release";
		if (export_format == EXPORT_FORMAT_AAB) {
			String bundle_build_command = vformat("bundle%s", build_type);
			cmdline.push_back(bundle_build_command);
		} else if (export_format == EXPORT_FORMAT_APK) {