### 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)

if (!is_inside_tree()) {
		tree_dirty = false;
		return;
	}
	if (tree->is_editing()) {
		return;
	}
	updating_tree = true;
	tree->clear();
	if (get_scene_node()) {
		_add_nodes(get_scene_node(), nullptr);
		last_hash = hash_djb2_one_64(0);
		_compute_hash(get_scene_node(), last_hash);
	}
	updating_tree = false;
	tree_dirty = false;
	if (!filter.strip_edges().is_empty() || !show_all_nodes) {
		_update_filter(nullptr, p_scroll_to_selected);
	}
}
bool SceneTreeEditor::_update_filter(TreeItem *p_parent, bool p_scroll_to_selected) {