### 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)

filter = p_filter;
	_update_filter(nullptr, true);
}
String SceneTreeEditor::get_filter() const {
	return filter;
}
String SceneTreeEditor::get_filter_term_warning() {
	return filter_term_warning;
}
void SceneTreeEditor::set_show_all_nodes(bool p_show_all_nodes) {
	show_all_nodes = p_show_all_nodes;
	_update_filter(nullptr, true);
}
void SceneTreeEditor::set_as_scene_tree_dock() {
	is_scene_tree_dock = true;
}
void SceneTreeEditor::set_display_foreign_nodes(bool p_display) {
	display_foreign = p_display;
	_update_tree();
}
void SceneTreeEditor::set_valid_types(const Vector<StringName> &p_valid) {
	valid_types = p_valid;
}
void SceneTreeEditor::set_editor_selection(EditorSelection *p_selection) {
	editor_selection = p_selection;
	tree->set_select_mode(Tree::SELECT_MULTI);
	tree->set_cursor_can_exit_tree(false);
	editor_selection->connect("selection_changed", callable_mp(this, &SceneTreeEditor::_selection_changed));
}
void SceneTreeEditor::_update_selection(TreeItem *item) {