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/main.py

@@ -16,12 +16,24 @@ from app.schemas import (
     ParticipantCreate,
     ParticipantResponse,
     SyncResponse,
+    ScheduleRequest,
 )
+from app.scheduler import start_scheduler, stop_scheduler
+from app.email_service import send_meeting_invite
+from app.zulip_service import send_zulip_notification
+from contextlib import asynccontextmanager
+from datetime import datetime, timezone, timedelta
 
 logging.basicConfig(level=logging.INFO)
 logger = logging.getLogger(__name__)
 
-app = FastAPI(title="Common Availability API")
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    start_scheduler()
+    yield
+    stop_scheduler()
+
+app = FastAPI(title="Common Availability API", lifespan=lifespan)
 
 app.add_middleware(
     CORSMiddleware,
@@ -57,7 +69,8 @@ async def create_participant(
     await db.refresh(participant)
 
     try:
-        await sync_participant_calendar(db, participant)
+        if participant.ics_url:
+            await sync_participant_calendar(db, participant)
     except Exception as e:
         logger.warning(f"Initial sync failed for {participant.email}: {e}")
 
@@ -121,7 +134,57 @@ async def sync_participant(participant_id: UUID, db: AsyncSession = Depends(get_
         raise HTTPException(status_code=404, detail="Participant not found")
 
     try:
-        count = await sync_participant_calendar(db, participant)
-        return {"status": "success", "blocks_synced": count}
+        if participant.ics_url:
+            count = await sync_participant_calendar(db, participant)
+            return {"status": "success", "blocks_synced": count}
+        return {"status": "skipped", "message": "No ICS URL provided"}
     except Exception as e:
         raise HTTPException(status_code=500, detail=str(e))
+
+
+@app.post("/api/schedule")
+async def schedule_meeting(
+    data: ScheduleRequest, db: AsyncSession = Depends(get_db)
+):
+    # 1. Validate Lead Time (2 hours)
+    min_start_time = datetime.now(timezone.utc) + timedelta(hours=2)
+    if data.start_time.replace(tzinfo=timezone.utc) < min_start_time:
+        raise HTTPException(
+            status_code=400, 
+            detail="Meetings must be scheduled at least 2 hours in advance."
+        )
+
+    # 2. Fetch Participants
+    result = await db.execute(
+        select(Participant).where(Participant.id.in_(data.participant_ids))
+    )
+    participants = result.scalars().all()
+    
+    if len(participants) != len(data.participant_ids):
+        raise HTTPException(status_code=400, detail="Some participants not found")
+
+    participant_dicts = [
+        {"name": p.name, "email": p.email} for p in participants
+    ]
+    participant_names = [p.name for p in participants]
+
+    # 3. Send Notifications
+    email_success = await send_meeting_invite(
+        participant_dicts,
+        data.title,
+        data.description,
+        data.start_time,
+        data.end_time
+    )
+
+    zulip_success = send_zulip_notification(
+        data.title,
+        data.start_time,
+        participant_names
+    )
+
+    return {
+        "status": "success",
+        "email_sent": email_success,
+        "zulip_sent": zulip_success
+    }