Update: Redmond Pie (the site I linked to, above) obviously didn’t do their homework. They stated that both the iOS and the Android versions of the Pokémon GO update were live. Many sites are now reporting that only the Android version of the update is trickling out. The iOS version is apparently still stuck in App Approval Hell.
I will update this thread when I personally see the update available on my iPhone app updates screen.
Speaking of the update, there is a fantastic easter egg in the new version.
If you walk 10 kilometers with Pikachu as your buddy, he will jump off the ground and onto your shoulder!