Currently this logic is implemented as part of a Response message, which includes a status code

I think the logic should be extracted to just be about serializing an arbitrary byte array so that it has a constant size. Also the current implementation uses the same object to represent both a padded and unpadded response (since this is done by calling the pad method, not in the constructor). This seems error prone from a type safety point of view, since forgetting to pad the content would not be noticeable at the type level.