### 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)

hide();
}
void SceneTreeDialog::_select() {
	if (tree->get_selected()) {
		// The signal may cause another dialog to be displayed, so be sure to hide this one first.
		hide();
		emit_signal(SNAME("selected"), tree->get_selected()->get_path());
	}
}
void SceneTreeDialog::_selected_changed() {
	get_ok_button()->set_disabled(!tree->get_selected());
}
void SceneTreeDialog::_filter_changed(const String &p_filter) {
	tree->set_filter(p_filter);
}
void SceneTreeDialog::_bind_methods() {
	ClassDB::bind_method("_cancel", &SceneTreeDialog::_cancel);
	ADD_SIGNAL(MethodInfo("selected", PropertyInfo(Variant::NODE_PATH, "path")));
}
SceneTreeDialog::SceneTreeDialog() {
	set_title(TTR("Select a Node"));
	content = memnew(VBoxContainer);
	add_child(content);