### Godot version

4.1???- 4.1.beta1 - 4.1.beta3 - 030c1a950e8cee19e72104b4fb79caba17a2d678

### System information

Tested only Linux versions.

### Issue description

**Regression from 4.0.3.stable:**
In the editor UI set the  `Node->process_mode` to `Disabled` or `When Paused`-> in the scene editor the subtree is grayed out. Save the scene and close the editor. 
It doesn*t need to be the current scene. 
Start it again, the subtree in the scene is no longer gray. The *.tscn file is updated correctly, e.g.:
```
  [node name="Node2D" type="Node2D"]
+process_mode = 4
```
 Workaround is to toggle the process mode again,
 close and open or reload the scene,
(or disable the `interface/scene_tabs/restore_scenes_on_load` option ...)

### Image gallery
![image](https://github.com/godotengine/godot/assets/4047289/b6a90b34-c9ec-4380-b953-f1e64cf72934)
![image](https://github.com/godotengine/godot/assets/4047289/978d4ab1-553b-49e6-bb76-6b18c22a942b)
![image](https://github.com/godotengine/godot/assets/4047289/4254f160-75d5-4186-9802-53b487d8d2f3)

error->set_meta("same_unique_name", true);
			}
		} else {
			error->set_text(text);
			error->set_meta("same_unique_name", true);
			error->set_meta("invalid_character", false);
			error->popup_centered();
		}
		item->set_text(0, p_node->get_name());
		return;
	}
	if (!is_scene_tree_dock) {
		p_node->set_name(new_name);
		item->set_metadata(0, p_node->get_path());
		emit_signal(SNAME("node_renamed"));
	} else {
		EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
		undo_redo->create_action("Rename Node", UndoRedo::MERGE_DISABLE, p_node);
		emit_signal(SNAME("node_prerename"), p_node, new_name);
		undo_redo->add_undo_method(p_node, "set_name", p_node->get_name());
		undo_redo->add_undo_method(item, "set_metadata", 0, p_node->get_path());
		undo_redo->add_undo_method(item, "set_text", 0, p_node->get_name());
		p_node->set_name(new_name);
		undo_redo->add_do_method(p_node, "set_name", new_name);
		undo_redo->add_do_method(item, "set_metadata", 0, p_node->get_path());
		undo_redo->add_do_method(item, "set_text", 0, new_name);
		undo_redo->commit_action();
	}
}
void SceneTreeEditor::_renamed() {