Merci pour la réponse, but at around 16:00 i.e. around 30 minutes of writing this question air play showed up proprely with mirroring as an option!
So it is working now, i am playing music on my Apple TV/tv set at the same time I have Pages running, great!
Of course, the music jumps when you do that but its ok.
I guess Numbers or Pages other apps will work great.