Thanks for the Playstation app!!
I wanted to get this feature request in the door as soon as I saw the note that Last.fm integration (i.e. scrobbling) is not supported. Is this on the feature roadmap? (Is there a feature roadmap for the Playstation app?) Thanks!
Updated on 2019-07-12
Sorry for the delay on this one.
As @hans-jürgen has mentioned, scrobbling is now works when you play tracks on Playstation.
You can check out the Last.FM update here.