### 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)

item->set_custom_color(0, get_theme_color(SNAME("warning_color"), SNAME("Editor")));
		}
	} else 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_selectable(0, marked_selectable);
		item->set_custom_color(0, get_theme_color(SNAME("accent_color"), SNAME("Editor")));
	} else if (!p_node->can_process()) {
		item->set_custom_color(0, get_theme_color(SNAME("disabled_font_color"), SNAME("Editor")));
	} else if (!marked_selectable && !marked_children_selectable) {
		Node *node = p_node;
		while (node) {
			if (marked.has(node)) {
				item->set_selectable(0, false);
				item->set_custom_color(0, get_theme_color(SNAME("error_color"), SNAME("Editor")));
				break;
			}
			node = node->get_parent();
		}
	}
	if (can_rename) { 
		String conf_warning = p_node->get_configuration_warnings_as_string();
		if (!conf_warning.is_empty()) {
			const int num_warnings = p_node->get_configuration_warnings().size();
			String warning_icon;
			if (num_warnings == 1) {
				warning_icon = SNAME("NodeWarning");