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/email_service.py

@@ -0,0 +1,82 @@
+import logging
+import uuid
+from datetime import datetime, timezone
+import aiosmtplib
+from email.message import EmailMessage
+from icalendar import Calendar, Event, vCalAddress, vText
+from app.config import settings
+
+logger = logging.getLogger(__name__)
+
+async def send_meeting_invite(
+    participants: list[dict],
+    title: str,
+    description: str,
+    start_time: datetime,
+    end_time: datetime,
+) -> bool:
+    if not settings.smtp_host or not settings.smtp_user or not settings.smtp_password:
+        logger.warning("SMTP credentials not configured. Skipping email invite.")
+        return False
+
+    # Create the ICS content
+    cal = Calendar()
+    cal.add('prodid', '-//Common Availability//m.com//')
+    cal.add('version', '2.0')
+    cal.add('method', 'REQUEST')
+
+    event = Event()
+    event.add('summary', title)
+    event.add('dtstart', start_time)
+    event.add('dtend', end_time)
+    event.add('dtstamp', datetime.now(timezone.utc))
+    event.add('description', description)
+    event.add('uid', str(uuid.uuid4()))
+    event.add('organizer', vCalAddress(f'MAILTO:{settings.smtp_user}'))
+
+    attendee_emails = []
+    for p in participants:
+        attendee = vCalAddress(f'MAILTO:{p["email"]}')
+        attendee.params['cn'] = vText(p["name"])
+        attendee.params['ROLE'] = vText('REQ-PARTICIPANT')
+        event.add('attendee', attendee, encode=0)
+        attendee_emails.append(p["email"])
+
+    cal.add_component(event)
+    ics_data = cal.to_ical()
+
+    # Create Email
+    msg = EmailMessage()
+    msg["Subject"] = f"Invitation: {title}"
+    msg["From"] = settings.smtp_user
+    msg["To"] = ", ".join(attendee_emails)
+    msg.set_content(
+        f"You have been invited to: {title}\n"
+        f"When: {start_time.strftime('%Y-%m-%d %H:%M %Z')}\n\n"
+        f"{description}"
+    )
+
+    # Attach ICS
+    msg.add_attachment(
+        ics_data,
+        maintype="text",
+        subtype="calendar",
+        filename="invite.ics",
+        params={"method": "REQUEST"}
+    )
+
+    # Send
+    try:
+        await aiosmtplib.send(
+            msg,
+            hostname=settings.smtp_host,
+            port=settings.smtp_port,
+            username=settings.smtp_user,
+            password=settings.smtp_password,
+            start_tls=True
+        )
+        logger.info(f"Sent meeting invites to {len(attendee_emails)} participants")
+        return True
+    except Exception as e:
+        logger.error(f"Failed to send email invite: {e}")
+        return False