feat: add email, scheduler, and Zulip integration services

- Add email service for sending meeting invites with ICS attachments
- Add scheduler for background calendar sync jobs
- Add Zulip service for meeting notifications
- Make ics_url optional for participants
- Add /api/schedule endpoint with 2-hour lead time validation
- Update frontend to support scheduling flow

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/src/app/availability_service.py

@@ -96,7 +96,7 @@ async def calculate_availability(
                 availability = "none"
 
             slots.append({
-                "day": day_name,
+                "day": slot_start.strftime("%Y-%m-%d"),
                 "hour": hour,
                 "availability": availability,
                 "availableParticipants": available_participants,