The school has provided the contracted service when the training is complete and a recommendation for test has been made iaw JAR-FCL 1.080(e).
How many PPL packages include the exam? In other words, you pay the school for, amongst other things, the exam (examiner, plane, whatever) and the school pays the examiner, fuel supplier and whatnot. At least, that was the case when I did my PPL training. I did not engage in a separate contract of any kind with the examiner, and I certainly did not pay the examiner directly.
So in that case the legal contract is between the student and the school, and the school would be the first to hear from me if something like this went wrong.