Send booking update when staff blockout is removed

Deleted staff blockouts aren't pushed to booking endpoints, creating apparent availability and risking double bookings. Keep availability synced so front-desk can confirm slots same day.

Overview

When a staff blockout is removed but not propagated, front-desk sees stale availability and risks double-bookings that frustrate clients. This flow pushes deletion events to downstream booking endpoints so managers and coordinators see accurate slots and can confirm appointments within minutes.