### 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 build_command;
#ifdef WINDOWS_ENABLED
		build_command = "gradlew.bat";
#else
		build_command = "gradlew";
#endif
		String build_path = ProjectSettings::get_singleton()->get_resource_path().path_join("android/build");
		build_command = build_path.path_join(build_command);
		String package_name = get_package_name(p_preset->get("package/unique_name"));
		String version_code = itos(p_preset->get("version/code"));
		String version_name = p_preset->get_version("version/name");
		String min_sdk_version = p_preset->get("gradle_build/min_sdk");
		if (!min_sdk_version.is_valid_int()) {
			min_sdk_version = itos(VULKAN_MIN_SDK_VERSION);
		}
		String target_sdk_version = p_preset->get("gradle_build/target_sdk");
		if (!target_sdk_version.is_valid_int()) {
			target_sdk_version = itos(DEFAULT_TARGET_SDK_VERSION);
		}
		String enabled_abi_string = join_abis(enabled_abis, "|", false);
		String sign_flag = should_sign ? "true" : "false";
		String zipalign_flag = "true";
		Vector<String> android_libraries;
		Vector<String> android_dependencies;
		Vector<String> android_dependencies_maven_repos;
#ifndef DISABLE_DEPRECATED
		Vector<PluginConfigAndroid> enabled_plugins = get_enabled_plugins(p_preset);
		PluginConfigAndroid::get_plugins_binaries(PluginConfigAndroid::BINARY_TYPE_LOCAL, enabled_plugins, android_libraries);
		PluginConfigAndroid::get_plugins_binaries(PluginConfigAndroid::BINARY_TYPE_REMOTE, enabled_plugins, android_dependencies);
		PluginConfigAndroid::get_plugins_custom_maven_repos(enabled_plugins, android_dependencies_maven_repos);