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/api/client.ts

@@ -4,7 +4,7 @@ export interface ParticipantAPI {
   id: string;
   name: string;
   email: string;
-  ics_url: string;
+  ics_url: string | null;
   created_at: string;
   updated_at: string;
 }
@@ -19,7 +19,7 @@ export interface TimeSlotAPI {
 export interface CreateParticipantRequest {
   name: string;
   email: string;
-  ics_url: string;
+  ics_url?: string;
 }
 
 async function handleResponse<T>(response: Response): Promise<T> {
@@ -76,3 +76,24 @@ export async function syncParticipant(id: string): Promise<void> {
     throw new Error('Failed to sync participant calendar');
   }
 }
+
+export async function scheduleMeeting(
+  participantIds: string[],
+  title: string,
+  description: string,
+  startTime: string,
+  endTime: string,
+): Promise<{ email_sent: boolean; zulip_sent: boolean }> {
+  const response = await fetch(`${API_URL}/api/schedule`, {
+    method: 'POST',
+    headers: { 'Content-Type': 'application/json' },
+    body: JSON.stringify({
+      participant_ids: participantIds,
+      title,
+      description,
+      start_time: startTime,
+      end_time: endTime,
+    }),
+  });
+  return handleResponse(response);
+}