### 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)

float opacity_step = 1.0f / list_max;
	float opacity_item = 1.0f;
	for (int i = 0; i < selected_nodes.size(); i++) {
		if (i < list_max) {
			HBoxContainer *hb = memnew(HBoxContainer);
			TextureRect *tf = memnew(TextureRect);
			int icon_size = get_theme_constant(SNAME("class_icon_size"), SNAME("Editor"));
			tf->set_custom_minimum_size(Size2(icon_size, icon_size));
			tf->set_stretch_mode(TextureRect::STRETCH_KEEP_ASPECT_CENTERED);
			tf->set_expand_mode(TextureRect::EXPAND_IGNORE_SIZE);
			tf->set_texture(icons[i]);
			hb->add_child(tf);
			Label *label = memnew(Label(selected_nodes[i]->get_name()));
			hb->add_child(label);
			vb->add_child(hb);
			hb->set_modulate(Color(1, 1, 1, opacity_item));
			opacity_item -= opacity_step;
		}
		NodePath p = selected_nodes[i]->get_path();
		objs.push_back(p);
	}
	set_drag_preview(vb);
	Dictionary drag_data;
	drag_data["type"] = "nodes";
	drag_data["nodes"] = objs;
	tree->set_drop_mode_flags(Tree::DROP_MODE_INBETWEEN | Tree::DROP_MODE_ON_ITEM);
	emit_signal(SNAME("nodes_dragged"));
	return drag_data;
}
bool SceneTreeEditor::_is_script_type(const StringName &p_type) const {