### 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)

TreeItem *which = tree->get_edited();
	ERR_FAIL_COND(!which);
	NodePath np = which->get_metadata(0);
	Node *n = get_node(np);
	ERR_FAIL_COND(!n);
	String new_name = which->get_text(0);
	_rename_node(n, new_name);
}
Node *SceneTreeEditor::get_selected() {
	return selected;
}
void SceneTreeEditor::set_marked(const HashSet<Node *> &p_marked, bool p_selectable, bool p_children_selectable) {
	if (tree_dirty) {
		_update_tree();
	}
	marked = p_marked;
	marked_selectable = p_selectable;
	marked_children_selectable = p_children_selectable;
	_update_tree();
}
void SceneTreeEditor::set_marked(Node *p_marked, bool p_selectable, bool p_children_selectable) {
	HashSet<Node *> s;
	if (p_marked) {
		s.insert(p_marked);
	}
	set_marked(s, p_selectable, p_children_selectable);
}
void SceneTreeEditor::set_filter(const String &p_filter) {