### 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)

for (int i = 0; i < properties.size(); i++) {
		p_list->push_back(PropertyInfo(Variant::STRING, "properties/" + itos(i) + "/path", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR | PROPERTY_USAGE_INTERNAL));
		p_list->push_back(PropertyInfo(Variant::STRING, "properties/" + itos(i) + "/spawn", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR | PROPERTY_USAGE_INTERNAL));
		p_list->push_back(PropertyInfo(Variant::STRING, "properties/" + itos(i) + "/sync", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR | PROPERTY_USAGE_INTERNAL));
		p_list->push_back(PropertyInfo(Variant::STRING, "properties/" + itos(i) + "/watch", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR | PROPERTY_USAGE_INTERNAL));
	}
}
TypedArray<NodePath> SceneReplicationConfig::get_properties() const {
	TypedArray<NodePath> paths;
	for (const ReplicationProperty &prop : properties) {
		paths.push_back(prop.name);
	}
	return paths;
}
void SceneReplicationConfig::add_property(const NodePath &p_path, int p_index) {