### 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)

tree->connect("multi_selected", callable_mp(this, &SceneTreeEditor::_cell_multi_selected));
	tree->connect("button_clicked", callable_mp(this, &SceneTreeEditor::_cell_button_pressed));
	tree->connect("nothing_selected", callable_mp(this, &SceneTreeEditor::_deselect_items));
	error = memnew(AcceptDialog);
	add_child(error);
	warning = memnew(AcceptDialog);
	add_child(warning);
	warning->set_title(TTR("Node Configuration Warning!"));
	last_hash = 0;
	blocked = 0;
	update_timer = memnew(Timer);
	update_timer->connect("timeout", callable_mp(this, &SceneTreeEditor::_update_tree).bind(false));
	update_timer->set_one_shot(true);
	update_timer->set_wait_time(0.5);
	add_child(update_timer);
	script_types = memnew(List<StringName>);
	ClassDB::get_inheriters_from_class("Script", script_types);
}
SceneTreeEditor::~SceneTreeEditor() {
	memdelete(script_types);
}
/******** DIALOG *********/
void SceneTreeDialog::popup_scenetree_dialog() {
	popup_centered_clamped(Size2(350, 700) * EDSCALE);
}
void SceneTreeDialog::_show_all_nodes_changed(bool p_button_pressed) {
	EditorSettings::get_singleton()->set_project_metadata("editor_metadata", "show_all_nodes_for_node_selection", p_button_pressed);
	tree->set_show_all_nodes(p_button_pressed);
}
void SceneTreeDialog::set_valid_types(const Vector<StringName> &p_valid) {