### 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
if ((int)Input::get_singleton()->get_mouse_button_mask() & 0x7) {
				log->add_message(TTR("Can't undo while mouse buttons are pressed."), EditorLog::MSG_TYPE_EDITOR);
			} else {
				EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
				String action = undo_redo->get_current_action_name();
				int id = undo_redo->get_current_action_history_id();
				if (!undo_redo->undo()) {
					log->add_message(TTR("Nothing to undo."), EditorLog::MSG_TYPE_EDITOR);
				} else if (!action.is_empty()) {
					switch (id) {
						case EditorUndoRedoManager::GLOBAL_HISTORY:
							log->add_message(vformat(TTR("Global Undo: %s"), action), EditorLog::MSG_TYPE_EDITOR);
							break;
						case EditorUndoRedoManager::REMOTE_HISTORY:
							log->add_message(vformat(TTR("Remote Undo: %s"), action), EditorLog::MSG_TYPE_EDITOR);
							break;
						default:
							log->add_message(vformat(TTR("Scene Undo: %s"), action), EditorLog::MSG_TYPE_EDITOR);
					}
				}
			}
		} break;
		case EDIT_REDO: {
			EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
			if ((int)Input::get_singleton()->get_mouse_button_mask() & 0x7) {
				log->add_message(TTR("Can't redo while mouse buttons are pressed."), EditorLog::MSG_TYPE_EDITOR);
			} else {
				if (!undo_redo->redo()) {
					log->add_message(TTR("Nothing to redo."), EditorLog::MSG_TYPE_EDITOR);
				} else {