### 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)

return name == p_to.name;
		}
		ReplicationProperty() {}
		ReplicationProperty(const NodePath &p_name) {
			name = p_name;
		}
	};
	List<ReplicationProperty> properties;
	List<NodePath> spawn_props;
	List<NodePath> sync_props;
	List<NodePath> watch_props;
protected:
	static void _bind_methods();
	bool _set(const StringName &p_name, const Variant &p_value);
	bool _get(const StringName &p_name, Variant &r_ret) const;
	void _get_property_list(List<PropertyInfo> *p_list) const;
public:
	TypedArray<NodePath> get_properties() const;
	void add_property(const NodePath &p_path, int p_index = -1);
	void remove_property(const NodePath &p_path);
	bool has_property(const NodePath &p_path) const;
	int property_get_index(const NodePath &p_path) const;
	bool property_get_spawn(const NodePath &p_path);
	void property_set_spawn(const NodePath &p_path, bool p_enabled);
	bool property_get_sync(const NodePath &p_path);
	void property_set_sync(const NodePath &p_path, bool p_enabled);
	bool property_get_watch(const NodePath &p_path);
	void property_set_watch(const NodePath &p_path, bool p_enabled);
	const List<NodePath> &get_spawn_properties() { return spawn_props; }