### 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)

if (!tree->get_root()) {
		return;
	}
	TreeItem *ti = tree->get_root()->get_first_child();
	while (ti) {
		if (ti->get_metadata(0).operator NodePath() == p_prop) {
			ti->set_checked(p_column, p_checked);
			return;
		}
		ti = ti->get_next();
	}
}
void ReplicationEditor::_update_config() {
	deleting = NodePath();
	tree->clear();
	tree->create_item();
	drop_label->set_visible(true);
	if (!config.is_valid()) {
		return;
	}
	TypedArray<NodePath> props = config->get_properties();
	if (props.size()) {
		drop_label->set_visible(false);
	}
	for (int i = 0; i < props.size(); i++) {
		const NodePath path = props[i];
		_add_property(path, config->property_get_spawn(path), config->property_get_sync(path), config->property_get_watch(path));
	}
}
void ReplicationEditor::edit(MultiplayerSynchronizer *p_sync) {