### 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
saving_resource = Ref<Resource>();
			ObjectID current_id = editor_history.get_current();
			Object *current_obj = current_id.is_valid() ? ObjectDB::get_instance(current_id) : nullptr;
			ERR_FAIL_NULL(current_obj);
			current_obj->notify_property_list_changed();
		} break;
		case SETTINGS_LAYOUT_SAVE: {
			if (p_file.is_empty()) {
				return;
			}
			Ref<ConfigFile> config;
			config.instantiate();
			Error err = config->load(EditorSettings::get_singleton()->get_editor_layouts_config());
			if (err == ERR_FILE_CANT_OPEN || err == ERR_FILE_NOT_FOUND) {
				config.instantiate();
			} else if (err != OK) {
				show_warning(TTR("An error occurred while trying to save the editor layout.\nMake sure the editor's user data path is writable."));
				return;
			}
			_save_docks_to_config(config, p_file);
			config->save(EditorSettings::get_singleton()->get_editor_layouts_config());
			layout_dialog->hide();
			_update_layouts_menu();
			if (p_file == "Default") {
				show_warning(TTR("Default editor layout overridden.\nTo restore the Default layout to its base settings, use the Delete Layout option and delete the Default layout."));
			}
		} break;
		case SETTINGS_LAYOUT_DELETE: {
			if (p_file.is_empty()) {
				return;