My best guesses, after looking at this code in 4.7:
WebServerDelegate seems to be used to push data to the PlayStation 4 companion app for “second-screen” functionality.
AssignStreamingChunk is still a mystery to me, but if I had to guess I’d say it has to do with optimizing the layout of optical media during cooking for efficient package loading at runtime.
AssignLayerChunkDelegate seems to be used for deciding which physical layer of e.g. a dual layer Blu-ray disc a chunk is cooked to.
ExtendedSaveGameInfoDelegate seems to be used for decorating saved games with platform-specific metadata like icons and descriptions, for e.g. console dashboards. Example: