### 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)

List<ReplicationProperty>::Element *E = properties.find(p_path);
	ERR_FAIL_COND_V(!E, false);
	return E->get().sync;
}
void SceneReplicationConfig::property_set_sync(const NodePath &p_path, bool p_enabled) {
	List<ReplicationProperty>::Element *E = properties.find(p_path);
	ERR_FAIL_COND(!E);
	if (E->get().sync == p_enabled) {
		return;
	}
	E->get().sync = p_enabled;
	sync_props.clear();
	for (const ReplicationProperty &prop : properties) {
		if (prop.sync) {
			sync_props.push_back(prop.name);
		}
	}
}
bool SceneReplicationConfig::property_get_watch(const NodePath &p_path) {
	List<ReplicationProperty>::Element *E = properties.find(p_path);
	ERR_FAIL_COND_V(!E, false);
	return E->get().watch;
}
void SceneReplicationConfig::property_set_watch(const NodePath &p_path, bool p_enabled) {