I have a vague memory of seeing an extract from some sort of TfL document which mapped schedules onto days of the year but it may be a false memory. If it exists and could be made available that would be a valuable addition, not just for school holidays but also for the special schedules which operate around Christmas.
For what it is worth, I suspect that knowing the actual school holidays may not be enough. I have heard it said that some operators do not bother to operate school holiday schedules on some routes at half term or on the few Christmas school holiday days where a Monday to Friday service operates. Also that if term starts on a Wednesday (say) some operators start the school day service on the Monday.
What I have heard said may be quite wrong but if it isn’t I would expect that they tell TfL what service they are going to operate!