### 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)

NodePath np = item->get_metadata(0);
	Node *n = get_node(np);
	if (!n) {
		return;
	}
	Dictionary d = p_data;
	if (String(d["type"]) == "nodes") {
		Array nodes = d["nodes"];
		emit_signal(SNAME("nodes_rearranged"), nodes, np, section);
	}
	if (String(d["type"]) == "files") {
		Vector<String> files = d["files"];
		String ftype = EditorFileSystem::get_singleton()->get_file_type(files[0]);
		if (_is_script_type(ftype)) {
			emit_signal(SNAME("script_dropped"), files[0], np);
		} else {
			emit_signal(SNAME("files_dropped"), files, np, section);
		}
	}
	if (String(d["type"]) == "script_list_element") {
		ScriptEditorBase *se = Object::cast_to<ScriptEditorBase>(d["script_list_element"]);
		if (se) {
			String sp = se->get_edited_resource()->get_path();
			if (_is_script_type(EditorFileSystem::get_singleton()->get_file_type(sp))) {
				emit_signal(SNAME("script_dropped"), sp, np);
			}
		}
	}
}
void SceneTreeEditor::_empty_clicked(const Vector2 &p_pos, MouseButton p_button) {