The Skype app for iPad has been updated today with support for iOS 9. Version 6.3 now supports Slide Over and Split View to have Skype chats next to other apps, quick text replies from notifications, and Spotlight search for usernames. Another update to Skype for iPad was released a while back bringing a redesigned UI for managing conversations, and I feel like the entire app has gotten considerably better over the past several months.
While I won't be able to stop using my Mac to record podcasts in the near future, I want to believe that my dream of having a full podcasting setup on iOS isn't so absurd anymore. Skype in Split View alongside Safari is a first step, but the road ahead is long (on my requirements list: Split View for Google Docs; the ability to plug a Rode microphone into my iPad; a way to record local audio during a Skype call).