### 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 (current == nullptr) {
		EditorNode::get_singleton()->show_warning(TTR("Select a replicator node in order to pick a property to add to it."));
		return;
	}
	Node *root = current->get_node(current->get_root_path());
	if (!root) {
		EditorNode::get_singleton()->show_warning(TTR("Not possible to add a new property to synchronize without a root."));
		return;
	}
	Dictionary d = p_data;
	if (!d.has("type")) {
		return;
	}
	String t = d["type"];
	if (t != "obj_property") {
		return;
	}
	Object *obj = d["object"];
	if (!obj) {
		return;
	}
	Node *node = Object::cast_to<Node>(obj);
	if (!node) {
		return;
	}
	String path = root->get_path_to(node);
	path += ":" + String(d["property"]);
	_add_sync_property(path);
}
void ReplicationEditor::_notification(int p_what) {