### 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 (show_all_nodes) {
		p_parent->set_visible(keep_for_children || keep);
	} else {
		// Show only selectable nodes, or parents of selectable.
		p_parent->set_visible(keep_for_children || selectable);
	}
	if (selectable) {
		p_parent->clear_custom_color(0);
		p_parent->set_selectable(0, true);
	} else if (keep_for_children) {
		p_parent->set_custom_color(0, get_theme_color(SNAME("disabled_font_color"), SNAME("Editor")));
		p_parent->set_selectable(0, false);
		p_parent->deselect(0);
	}
	if (editor_selection) {
		Node *n = get_node(p_parent->get_metadata(0));
		if (selectable) {
			if (p_scroll_to_selected && n && editor_selection->is_selected(n)) {
				tree->scroll_to_item(p_parent);
			}
		} else {
			if (n && p_parent->is_selected(0)) {
				editor_selection->remove_node(n);
				p_parent->deselect(0);
			}
		}
	}
	return p_parent->is_visible();
}
bool SceneTreeEditor::_item_matches_all_terms(TreeItem *p_item, PackedStringArray p_terms) {