### 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)

ERR_FAIL_COND(properties.find(p_path));
	if (p_index < 0 || p_index == properties.size()) {
		properties.push_back(ReplicationProperty(p_path));
		sync_props.push_back(p_path);
		spawn_props.push_back(p_path);
		return;
	}
	ERR_FAIL_INDEX(p_index, properties.size());
	List<ReplicationProperty>::Element *I = properties.front();
	int c = 0;
	while (c < p_index) {
		I = I->next();
		c++;
	}
	properties.insert_before(I, ReplicationProperty(p_path));
	sync_props.clear();
	spawn_props.clear();
	for (const ReplicationProperty &prop : properties) {
		if (prop.sync) {
			sync_props.push_back(prop.name);
		}
		if (prop.spawn) {
			spawn_props.push_back(prop.name);
		}
	}
}
void SceneReplicationConfig::remove_property(const NodePath &p_path) {