After research, I found a solution for my problem. Before I joined the exams, I always made sure that the camera settings match the requirements (for example, that the screen of my laptop is clearly visible in the camera, or that my workplace is visible).
Unfortunately, I did not close my camera before joining the meeting. I found out that the camera can only work with one application at a time. Of course it cannot work on Zoom, if I have already opened it.
I can recommend to everyone to make sure that the camera is not running (also make sure to close apps that use the camera), before joining a Zoom meeting where the camera is required.