### 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)

Node *root = current->get_node(current->get_root_path());
	ERR_FAIL_COND(!root);
	Node *node = get_node(p_path);
	ERR_FAIL_COND(!node);
	NodePath path_to = root->get_path_to(node);
	adding_node_path = path_to;
	prop_selector->select_property_from_instance(node);
}
void ReplicationEditor::_pick_new_property() {
	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;
	}
	pick_node->popup_scenetree_dialog();
	pick_node->get_filter_line_edit()->clear();
	pick_node->get_filter_line_edit()->grab_focus();
}
void ReplicationEditor::_add_sync_property(String p_path) {