### 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)

for (int i = 0; i < p_terms.size(); i++) {
		String term = p_terms[i];
		// Recognize special filter.
		if (term.contains(":") && !term.get_slicec(':', 0).is_empty()) {
			String parameter = term.get_slicec(':', 0);
			String argument = term.get_slicec(':', 1);
			if (parameter == "type" || parameter == "t") {
				// F
				String type = get_node(p_item->get_metadata(0))->get_class();
				bool term_in_inherited_class = false;
				// E
				while (type != "Node") {
					if (type.to_lower().contains(argument)) {
						term_in_inherited_class = true;
						break;
					}
					type = ClassDB::get_parent_class(type);
				}
				if (!term_in_inherited_class) {
					return false;
				}
			} else if (parameter == "group" || parameter == "g") {
				// F
				Node *node = get_node(p_item->get_metadata(0));
				if (argument.is_empty()) {
					// W
					if (node->get_persistent_group_count() == 0) {
						return false;
					}
				} else {