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>

frontend/src/components/ScheduleModal.tsx

@@ -1,5 +1,6 @@
 import { useState } from 'react';
 import { TimeSlot, Participant } from '@/types/calendar';
+import { scheduleMeeting } from '@/api/client';
 import {
   Dialog,
   DialogContent,
@@ -11,7 +12,7 @@ import { Input } from '@/components/ui/input';
 import { Textarea } from '@/components/ui/textarea';
 import { Label } from '@/components/ui/label';
 import { toast } from '@/hooks/use-toast';
-import { Calendar, Clock, Users, Send } from 'lucide-react';
+import { Calendar, Clock, Users, Send, AlertCircle } from 'lucide-react';
 
 interface ScheduleModalProps {
   isOpen: boolean;
@@ -34,7 +35,23 @@ export const ScheduleModal = ({
     return `${hour.toString().padStart(2, '0')}:00`;
   };
 
-  const handleSubmit = () => {
+  const formatDate = (dateStr: string) => {
+    const date = new Date(dateStr + 'T00:00:00');
+    return date.toLocaleDateString('en-US', { weekday: 'short', month: 'short', day: 'numeric' });
+  };
+
+  const isTooSoon = () => {
+    if (!slot) return false;
+    // Use UTC to match backend timezone
+    const startDateTime = new Date(`${slot.day}T${formatHour(slot.hour)}:00Z`);
+    const now = new Date();
+    const twoHoursFromNow = new Date(now.getTime() + 2 * 60 * 60 * 1000);
+    return startDateTime < twoHoursFromNow;
+  };
+
+  const tooSoon = isTooSoon();
+
+  const handleSubmit = async () => {
     if (!title.trim()) {
       toast({
         title: "Please enter a meeting title",
@@ -43,19 +60,41 @@ export const ScheduleModal = ({
       return;
     }
 
+    if (!slot) return;
+
     setIsSubmitting(true);
 
-    // Simulate API call
-    setTimeout(() => {
-      setIsSubmitting(false);
+    try {
+      // Calculate start and end times
+      // slot.day is YYYY-MM-DD
+      const startDateTime = new Date(`${slot.day}T${formatHour(slot.hour)}:00Z`);
+      const endDateTime = new Date(`${slot.day}T${formatHour(slot.hour + 1)}:00Z`);
+
+      await scheduleMeeting(
+        participants.map(p => p.id),
+        title,
+        notes,
+        startDateTime.toISOString(),
+        endDateTime.toISOString()
+      );
+
       toast({
         title: "Meeting scheduled",
-        description: "Invitations sent to all participants",
+        description: "Invitations sent via Email and Zulip",
       });
+
       setTitle('');
       setNotes('');
       onClose();
-    }, 1000);
+    } catch (error) {
+      toast({
+        title: "Scheduling failed",
+        description: error instanceof Error ? error.message : "Unknown error",
+        variant: "destructive",
+      });
+    } finally {
+      setIsSubmitting(false);
+    }
   };
 
   if (!slot) return null;
@@ -72,7 +111,7 @@ export const ScheduleModal = ({
           <div className="bg-accent/50 rounded-lg p-4 space-y-3">
             <div className="flex items-center gap-3 text-sm">
               <Calendar className="w-4 h-4 text-primary" />
-              <span className="font-medium">{slot.day}</span>
+              <span className="font-medium">{formatDate(slot.day)}</span>
             </div>
             <div className="flex items-center gap-3 text-sm">
               <Clock className="w-4 h-4 text-primary" />
@@ -109,12 +148,20 @@ export const ScheduleModal = ({
             </div>
           </div>
 
+          {/* Lead Time Warning */}
+          {tooSoon && (
+            <div className="flex items-center gap-2 p-3 bg-destructive/10 border border-destructive/20 rounded-lg text-sm text-destructive">
+              <AlertCircle className="w-4 h-4 flex-shrink-0" />
+              <span>Meetings must be scheduled at least 2 hours in advance</span>
+            </div>
+          )}
+
           {/* Actions */}
           <Button
             variant="schedule"
             className="w-full h-12"
             onClick={handleSubmit}
-            disabled={isSubmitting}
+            disabled={isSubmitting || tooSoon}
           >
             {isSubmitting ? (
               <span className="animate-pulse">Sending...</span>