### 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 (p_button != MouseButton::RIGHT) {
		return;
	}
	_rmb_select(p_pos);
}
void SceneTreeEditor::_rmb_select(const Vector2 &p_pos, MouseButton p_button) {
	if (p_button != MouseButton::RIGHT) {
		return;
	}
	emit_signal(SNAME("rmb_pressed"), tree->get_screen_position() + p_pos);
}
void SceneTreeEditor::update_warning() {
	_warning_changed(nullptr);
}
void SceneTreeEditor::_warning_changed(Node *p_for_node) {
	//should use a timer
	update_timer->start();
}
void SceneTreeEditor::set_auto_expand_selected(bool p_auto, bool p_update_settings) {
	if (p_update_settings) {
		EditorSettings::get_singleton()->set("docks/scene_tree/auto_expand_to_selected", p_auto);
	}
	auto_expand_selected = p_auto;
}
void SceneTreeEditor::set_connect_to_script_mode(bool p_enable) {