Moves the appointment with the given UID to a new start time, keeping the attendee and appointment type. The new slot is validated like a new booking; on conflict the API returns 400 and the agent should re-query /availability. The rescheduled appointment gets a new UID (returned in the response); the old UID is kept as rescheduled_from_uid. When no appointment with this UID exists the API returns 400 with error_code ResourceNotExist.