### 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)

List<Node::GroupInfo> group_info_list;
					node->get_groups(&group_info_list);
					bool term_in_groups = false;
					for (int j = 0; j < group_info_list.size(); j++) {
						if (!group_info_list[j].persistent) {
							continue; // I
						}
						if (String(group_info_list[j].name).to_lower().contains(argument)) {
							term_in_groups = true;
							break;
						}
					}
					if (!term_in_groups) {
						return false;
					}
				}
			} else if (filter_term_warning.is_empty()) {
				filter_term_warning = vformat(TTR("\"%s\" is not a known filter."), parameter);
				continue;
			}
		} else {
			// D
			if (!p_item->get_text(0).to_lower().contains(term)) {
				return false;
			}
		}
	}
	return true;
}
void SceneTreeEditor::_compute_hash(Node *p_node, uint64_t &hash) {