### 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 *item = Object::cast_to<TreeItem>(p_object);
	ERR_FAIL_COND(!item);
	if (!item->is_visible()) {
		return;
	}
	NodePath np = item->get_metadata(0);
	Node *n = get_node(np);
	if (!n) {
		return;
	}
	if (!editor_selection) {
		return;
	}
	if (p_selected) {
		editor_selection->add_node(n);
	} else {
		editor_selection->remove_node(n);
	}
	// Emitted "selected" in _selected_changed() when select single node, so select multiple node emit "changed"
	if (editor_selection->get_selected_nodes().size() > 1) {
		emit_signal(SNAME("node_changed"));
	}
}
void SceneTreeEditor::_notification(int p_what) {