### 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)

undo_redo->create_action(TTR("Set spawn property"));
		method = "property_set_spawn";
	} else if (column == 2) {
		undo_redo->create_action(TTR("Set sync property"));
		method = "property_set_sync";
	} else if (column == 3) {
		undo_redo->create_action(TTR("Set watch property"));
		method = "property_set_watch";
	} else {
		ERR_FAIL();
	}
	undo_redo->add_do_method(config.ptr(), method, prop, value);
	undo_redo->add_undo_method(config.ptr(), method, prop, !value);
	undo_redo->add_do_method(this, "_update_checked", prop, column, value);
	undo_redo->add_undo_method(this, "_update_checked", prop, column, !value);
	undo_redo->commit_action();
}
void ReplicationEditor::_tree_button_pressed(Object *p_item, int p_column, int p_id, MouseButton p_button) {
	if (p_button != MouseButton::LEFT) {
		return;
	}
	TreeItem *ti = Object::cast_to<TreeItem>(p_item);
	if (!ti) {
		return;
	}
	deleting = ti->get_metadata(0);
	delete_dialog->set_text(TTR("Delete Property?") + "\n\"" + ti->get_text(0) + "\"");
	delete_dialog->popup_centered();
}
void ReplicationEditor::_dialog_closed(bool p_confirmed) {