### 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
String action = undo_redo->get_current_action_name();
					if (action.is_empty()) {
						break;
					}
					switch (undo_redo->get_current_action_history_id()) {
						case EditorUndoRedoManager::GLOBAL_HISTORY:
							log->add_message(vformat(TTR("Global Redo: %s"), action), EditorLog::MSG_TYPE_EDITOR);
							break;
						case EditorUndoRedoManager::REMOTE_HISTORY:
							log->add_message(vformat(TTR("Remote Redo: %s"), action), EditorLog::MSG_TYPE_EDITOR);
							break;
						default:
							log->add_message(vformat(TTR("Scene Redo: %s"), action), EditorLog::MSG_TYPE_EDITOR);
					}
				}
			}
		} break;
		case EDIT_RELOAD_SAVED_SCENE: {
			Node *scene = get_edited_scene();
			if (!scene) {
				break;
			}
			String filename = scene->get_scene_file_path();
			if (filename.is_empty()) {
				show_warning(TTR("Can't reload a scene that was never saved."));
				break;
			}
			if (unsaved_cache && !p_confirmed) {
				confirmation->set_ok_button_text(TTR("Reload Saved Scene"));
				confirmation->set_text(