### 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)

drop_label->set_horizontal_alignment(HORIZONTAL_ALIGNMENT_CENTER);
	drop_label->set_vertical_alignment(VERTICAL_ALIGNMENT_CENTER);
	tree->add_child(drop_label);
	drop_label->set_anchors_and_offsets_preset(Control::PRESET_FULL_RECT);
	SET_DRAG_FORWARDING_CDU(tree, ReplicationEditor);
}
void ReplicationEditor::_bind_methods() {
	ClassDB::bind_method(D_METHOD("_update_config"), &ReplicationEditor::_update_config);
	ClassDB::bind_method(D_METHOD("_update_checked", "property", "column", "checked"), &ReplicationEditor::_update_checked);
}
bool ReplicationEditor::_can_drop_data_fw(const Point2 &p_point, const Variant &p_data, Control *p_from) const {
	Dictionary d = p_data;
	if (!d.has("type")) {
		return false;
	}
	String t = d["type"];
	if (t != "obj_property") {
		return false;
	}
	Object *obj = d["object"];
	if (!obj) {
		return false;
	}
	Node *node = Object::cast_to<Node>(obj);
	if (!node) {
		return false;
	}
	return true;
}
void ReplicationEditor::_drop_data_fw(const Point2 &p_point, const Variant &p_data, Control *p_from) {