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/config.py

@@ -6,6 +6,18 @@ class Settings(BaseSettings):
     sync_database_url: str = "postgresql://postgres:postgres@db:5432/availability"
     ics_refresh_interval_minutes: int = 15
 
+    # SMTP Settings
+    smtp_host: str | None = None
+    smtp_port: int = 587
+    smtp_user: str | None = None
+    smtp_password: str | None = None
+
+    # Zulip Settings
+    zulip_site: str | None = None
+    zulip_email: str | None = None
+    zulip_api_key: str | None = None
+    zulip_stream: str = "general"
+
     class Config:
         env_file = ".env"