The post is already a few days old, but if anyone else encounters the same problem, I found the error using the solution described above.
The example in the documentation is still incorrect for the request.
The data for the appointment is specified as “start” and “end” in the demo body. However, the correct format is "startDateTime" and “endDateTime” in the JSON body.
After making this change, I was also able to omit optional parts of the request object and got the desired responses.