The Apple TV Generation 3 has been malfunctioning for over a week - and there is no solution.
https://www.golem.de/news/streaming-airplay-beim-apple-tv-generation-3-gestoert-2111-160892.html
Please keep in mind that especially with new devices and new software, the desired good result is not always achieved immediately and a non-functioning Airplay can also affect other applications.
Surely this message can also be found in other language areas.