There is. The fitness app has the classes and the watch even temporarily syncs with the AppleTV instead of the phone during the workout. The integration is very easy.
That main photo is REALLY MISLEADING and should be changed. When you use AirPlay 2 to stream an Apple Fitness+ workout directly to TV, you ONLY get the audio and video, NONE of the metrics are displayed on the screen. Please fix this. 🙁