### 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)

print_verbose("Checking build version...");
			Ref<FileAccess> f = FileAccess::open("res://android/.build_version", FileAccess::READ);
			if (f.is_null()) {
				add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), TTR("Trying to build from a gradle built template, but no version info for it exists. Please reinstall from the 'Project' menu."));
				return ERR_UNCONFIGURED;
			}
			String version = f->get_line().strip_edges();
			print_verbose("- build version: " + version);
			if (version != VERSION_FULL_CONFIG) {
				add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Android build version mismatch: Template installed: %s, Godot version: %s. Please reinstall Android build template from 'Project' menu."), version, VERSION_FULL_CONFIG));
				return ERR_UNCONFIGURED;
			}
		}
		const String assets_directory = get_assets_directory(p_preset, export_format);
		String sdk_path = EDITOR_GET("export/android/android_sdk_path");
		ERR_FAIL_COND_V_MSG(sdk_path.is_empty(), ERR_UNCONFIGURED, "Android SDK path must be configured in Editor Settings at 'export/android/android_sdk_path'.");
		print_verbose("Android sdk path: " + sdk_path);
		
		String project_name = get_project_name(p_preset->get("package/name"));
		err = _create_project_name_strings_files(p_preset, project_name); 
		if (err != OK) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), TTR("Unable to overwrite res://android/build/res/*.xml files with project name."));
		}
		
		_copy_icons_to_gradle_project(p_preset, processed_splash_config_xml, splash_image, splash_bg_color_image, main_image, foreground, background);
		
		_write_tmp_manifest(p_preset, p_give_internet, p_debug);
		
		_clear_assets_directory();
		_remove_copied_libs();