### 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)

r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "package/signed"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::INT, "package/app_category", PROPERTY_HINT_ENUM, "Accessibility,Audio,Game,Image,Maps,News,Productivity,Social,Video"), APP_CATEGORY_GAME));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "package/retain_data_on_uninstall"), false));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "package/exclude_from_recents"), false));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "package/show_in_android_tv"), false));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "package/show_in_app_library"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "package/show_as_launcher_app"), false));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, launcher_icon_option, PROPERTY_HINT_FILE, "*.png"), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, launcher_adaptive_icon_foreground_option, PROPERTY_HINT_FILE, "*.png"), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, launcher_adaptive_icon_background_option, PROPERTY_HINT_FILE, "*.png"), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "graphics/opengl_debug"), false));
	r_options->push_back(ExportOption(PropertyInfo(Variant::INT, "xr_features/xr_mode", PROPERTY_HINT_ENUM, "Regular,OpenXR"), XR_MODE_REGULAR, false, true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "screen/immersive_mode"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "screen/support_small"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "screen/support_normal"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "screen/support_large"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "screen/support_xlarge"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "user_data_backup/allow"), false));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "command_line/extra_args"), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "apk_expansion/enable"), false, false, true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "apk_expansion/SALT"), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "apk_expansion/public_key", PROPERTY_HINT_MULTILINE_TEXT), "", false, true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::PACKED_STRING_ARRAY, "permissions/custom_permissions"), PackedStringArray()));
	const char **perms = android_perms;
	while (*perms) {
		r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, vformat("%s/%s", PNAME("permissions"), String(*perms).to_lower())), false));
		perms++;
	}
}
String EditorExportPlatformAndroid::get_name() const {