### Godot version

4.1.dev4

### System information

Windows 10 Godot 4.1.dev4

### Issue description

The watched property in the Multiplayer Synchronizer node is supposed to pass the variable through the network only when it changes, but as I use the network profiler, it is evidently not working as intended

### Steps to reproduce

Open 2 debug instances on the project I will give, use the network profiler and you will see the variable does not change, although it goes up to 780b/s on the network

### Minimal reproduction project

[minimalproject.zip](https://github.com/godotengine/godot/files/11659414/minimalproject.zip)

String subpath = prop.substr(path.size());
		Node *node = root_node->get_node_or_null(path);
		if (!node) {
			node = root_node;
		}
		item->set_text(0, String(node->get_name()) + ":" + subpath);
		icon = _get_class_icon(node);
		bool valid = false;
		Variant value = node->get(subpath, &valid);
		if (valid && !can_sync(value)) {
			item->set_icon(3, get_theme_icon(SNAME("StatusWarning"), SNAME("EditorIcons")));
			item->set_tooltip_text(3, TTR("Property of this type not supported."));
		}
	}
	item->set_icon(0, icon);
	item->add_button(4, get_theme_icon(SNAME("Remove"), SNAME("EditorIcons")));
	item->set_text_alignment(1, HORIZONTAL_ALIGNMENT_CENTER);
	item->set_cell_mode(1, TreeItem::CELL_MODE_CHECK);
	item->set_checked(1, p_spawn);
	item->set_editable(1, true);
	item->set_text_alignment(2, HORIZONTAL_ALIGNMENT_CENTER);
	item->set_cell_mode(2, TreeItem::CELL_MODE_CHECK);
	item->set_checked(2, p_sync);
	item->set_editable(2, true);
	item->set_text_alignment(3, HORIZONTAL_ALIGNMENT_CENTER);
	item->set_cell_mode(3, TreeItem::CELL_MODE_CHECK);
	item->set_checked(3, p_watch);
	item->set_editable(3, true);
}