Continuity Camera video is mirrored (horizontally flipped), how to fix?

I want to use the Continuity Camera as a camera for my AppleTV 4K, that simultaneously shows what my iPhone sees. My AppleTV is connected to a beamer so I could make live footage on stage with this.

Unfortunately the image of this iPhone-camera is mirrored / flipped horizontal if used as Continuity Camera.

iOS only offers the possibility to mirror the front ("selfie") camera of an iPhone, not the regular camera with better quality used as a Continuity Camera.

Does anyone know a solution for this?

(AppleTV with tvOS 17, iPhone with iOS 17)