### 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)

} else if (num_warnings <= 3) {
				warning_icon = vformat("NodeWarnings%d", num_warnings);
			} else {
				warning_icon = SNAME("NodeWarnings4Plus");
			}
			
			const String bullet_point = U"•  ";
			int next_newline = 0;
			while (next_newline != -1) {
				next_newline = conf_warning.find("\n", next_newline + 2);
				if (conf_warning.substr(next_newline + 1, bullet_point.length()) != bullet_point) {
					conf_warning = conf_warning.insert(next_newline + 1, "    ");
				}
			}
			String newline = (num_warnings == 1 ? "\n" : "\n\n");
			item->add_button(0, get_theme_icon(warning_icon, SNAME("EditorIcons")), BUTTON_WARNING, false, TTR("Node configuration warning:") + newline + conf_warning);
		}
		if (p_node->is_unique_name_in_owner()) {
			item->add_button(0, get_theme_icon(SNAME("SceneUniqueName"), SNAME("EditorIcons")), BUTTON_UNIQUE, false, vformat(TTR("This node can be accessed from within anywhere in the scene by preceding it with the '%s' prefix in a node path.\nClick to disable this."), UNIQUE_NODE_PREFIX));
		}
		int num_connections = p_node->get_persistent_signal_connection_count();
		int num_groups = p_node->get_persistent_group_count();
		String msg_temp;
		if (num_connections >= 1) {
			Array arr;
			arr.push_back(num_connections);
			msg_temp += TTRN("Node has one connection.", "Node has {num} connections.", num_connections).format(arr, "{num}");
			if (num_groups >= 1) {
				msg_temp += "\n";
			}