feat: implement Phase 2 - Matches API with real-time notifications

Backend changes:
- Add matches API routes (POST, GET, PUT, DELETE)
- Create/accept/reject match requests
- Auto-create private chat rooms on match acceptance
- Socket.IO notifications for match events (received, accepted, cancelled)
- Users join personal rooms (user_{id}) for notifications

Frontend changes:
- Add MatchesPage component with inbox UI
- Matches navigation link with notification badge
- Real-time match request count updates
- Accept/reject match functionality
- Filter matches by status (all/pending/accepted)
- Integrate match requests in EventChatPage (UserPlus button)

Features:
- Send match requests to event participants
- Accept incoming match requests
- Real-time notifications via Socket.IO
- Automatic private chat room creation
- Match status tracking (pending/accepted/completed)
- Authorization checks (only participants can match)
- Duplicate match prevention

frontend/src/pages/EventChatPage.jsx

@@ -4,7 +4,7 @@ import Layout from '../components/layout/Layout';
 import { useAuth } from '../contexts/AuthContext';
 import { Send, UserPlus, Loader2, LogOut, AlertTriangle, QrCode, Edit2, Filter, X } from 'lucide-react';
 import { connectSocket, disconnectSocket, getSocket } from '../services/socket';
-import { eventsAPI, heatsAPI } from '../services/api';
+import { eventsAPI, heatsAPI, matchesAPI } from '../services/api';
 import HeatsBanner from '../components/heats/HeatsBanner';
 
 const EventChatPage = () => {
@@ -252,12 +252,29 @@ const EventChatPage = () => {
     }
   };
 
-  const handleMatchWith = (userId) => {
-    // TODO: Implement match request
-    alert(`Match request sent to user!`);
-    setTimeout(() => {
-      navigate(`/matches/1/chat`);
-    }, 1000);
+  const handleMatchWith = async (userId) => {
+    try {
+      const result = await matchesAPI.createMatch(userId, slug);
+
+      // Show success message
+      alert(`Match request sent successfully! The user will be notified.`);
+
+      // Optional: Navigate to matches page or refresh matches list
+      // For now, we just show a success message
+    } catch (error) {
+      console.error('Failed to send match request:', error);
+
+      // Show appropriate error message
+      if (error.status === 400 && error.message.includes('already exists')) {
+        alert('You already have a match request with this user.');
+      } else if (error.status === 403) {
+        alert('You must be a participant of this event to send match requests.');
+      } else if (error.status === 404) {
+        alert('Event not found.');
+      } else {
+        alert('Failed to send match request. Please try again.');
+      }
+    }
   };
 
   const handleHeatsSave = () => {