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/models.py

@@ -18,7 +18,7 @@ class Participant(Base):
     )
     name: Mapped[str] = mapped_column(String(255), nullable=False)
     email: Mapped[str] = mapped_column(String(255), nullable=False, unique=True)
-    ics_url: Mapped[str] = mapped_column(Text, nullable=False)
+    ics_url: Mapped[str | None] = mapped_column(Text, nullable=True)
     created_at: Mapped[datetime] = mapped_column(
         DateTime, default=datetime.utcnow, nullable=False
     )