### 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)

class TextureRect;
class SceneTreeEditor : public Control {
	GDCLASS(SceneTreeEditor, Control);
	EditorSelection *editor_selection = nullptr;
	enum SceneTreeEditorButton {
		BUTTON_SUBSCENE = 0,
		BUTTON_VISIBILITY = 1,
		BUTTON_SCRIPT = 2,
		BUTTON_LOCK = 3,
		BUTTON_GROUP = 4,
		BUTTON_WARNING = 5,
		BUTTON_SIGNALS = 6,
		BUTTON_GROUPS = 7,
		BUTTON_PIN = 8,
		BUTTON_UNIQUE = 9,
	};
	Tree *tree = nullptr;
	Node *selected = nullptr;
	ObjectID instance_node;
	String filter;
	String filter_term_warning;
	bool show_all_nodes = false;
	AcceptDialog *error = nullptr;
	AcceptDialog *warning = nullptr;
	bool auto_expand_selected = true;
	bool connect_to_script_mode = false;
	bool connecting_signal = false;
	int blocked;
	void _compute_hash(Node *p_node, uint64_t &hash);
	void _add_nodes(Node *p_node, TreeItem *p_parent);