### 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)

}
	Ref<Texture2D> icon = EditorNode::get_singleton()->get_object_icon(p_node, "Node");
	item->set_icon(0, icon);
	item->set_metadata(0, p_node->get_path());
	if (connect_to_script_mode) {
		Color accent = get_theme_color(SNAME("accent_color"), SNAME("Editor"));
		Ref<Script> scr = p_node->get_script();
		if (!scr.is_null() && EditorNode::get_singleton()->get_object_custom_type_base(p_node) != scr) {
			
			item->add_button(0, get_theme_icon(SNAME("Script"), SNAME("EditorIcons")), BUTTON_SCRIPT);
		} else {
			
			item->set_custom_color(0, get_theme_color(SNAME("disabled_font_color"), SNAME("Editor")));
			item->set_selectable(0, false);
			if (!scr.is_null()) { 
				item->add_button(0, get_theme_icon(SNAME("Script"), SNAME("EditorIcons")), BUTTON_SCRIPT);
				item->set_button_disabled(0, item->get_button_count(0) - 1, true);
			}
			accent.a *= 0.7;
		}
		if (marked.has(p_node)) {
			String node_name = p_node->get_name();
			if (connecting_signal) {
				node_name += " " + TTR("(Connecting From)");
			}
			item->set_text(0, node_name);
			item->set_custom_color(0, accent);
		}
	} else if (part_of_subscene) {
		if (valid_types.size() == 0) {