### 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 (!can_rename) {
		return Variant(); //not editable tree
	}
	if (tree->get_button_id_at_position(p_point) != -1) {
		return Variant(); //dragging from button
	}
	Vector<Node *> selected_nodes;
	Vector<Ref<Texture2D>> icons;
	TreeItem *next = tree->get_next_selected(nullptr);
	while (next) {
		NodePath np = next->get_metadata(0);
		Node *n = get_node(np);
		if (n) {
			// O
			if (!n->get_owner() || n->get_owner() == get_scene_node() || n->get_owner()->get_scene_file_path().is_empty()) {
				selected_nodes.push_back(n);
				icons.push_back(next->get_icon(0));
			}
		}
		next = tree->get_next_selected(next);
	}
	if (selected_nodes.is_empty()) {
		return Variant();
	}
	VBoxContainer *vb = memnew(VBoxContainer);
	Array objs;
	int list_max = 10;