### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
_save_scene_with_preview(p_file);
				project_run_bar->play_main_scene((bool)pick_main_scene->get_meta("from_native", false));
			}
		} break;
		case FILE_EXPORT_MESH_LIBRARY: {
			Ref<MeshLibrary> ml;
			if (file_export_lib_merge->is_pressed() && FileAccess::exists(p_file)) {
				ml = ResourceLoader::load(p_file, "MeshLibrary");
				if (ml.is_null()) {
					show_accept(TTR("Can't load MeshLibrary for merging!"), TTR("OK"));
					return;
				}
			}
			if (ml.is_null()) {
				ml = Ref<MeshLibrary>(memnew(MeshLibrary));
			}
			MeshLibraryEditor::update_library_file(editor_data.get_edited_scene_root(), ml, true, file_export_lib_apply_xforms->is_pressed());
			Error err = ResourceSaver::save(ml, p_file);
			if (err) {
				show_accept(TTR("Error saving MeshLibrary!"), TTR("OK"));
				return;
			} else if (ResourceCache::has(p_file)) {
				
				ResourceLoader::load(p_file)->reload_from_file();
			}
		} break;
		case RESOURCE_SAVE:
		case RESOURCE_SAVE_AS: {
			ERR_FAIL_COND(saving_resource.is_null());
			save_resource_in_path(saving_resource, p_file);