feat: integrate NextAuth.js for authentication, update database service to use better-sqlite3 adapter, and enhance header component with user session management

src/app/api/auth/[...nextauth]/route.ts

@@ -0,0 +1,4 @@
+import { handlers } from '@/lib/auth';
+
+export const { GET, POST } = handlers;
+

src/app/api/auth/register/route.ts

@@ -0,0 +1,25 @@
+import { NextResponse } from 'next/server';
+import { registerUser } from '@/services/auth';
+
+export async function POST(request: Request) {
+  try {
+    const body = await request.json();
+    const { email, password, name } = body;
+
+    if (!email || !password) {
+      return NextResponse.json({ error: 'Email et mot de passe requis' }, { status: 400 });
+    }
+
+    const result = await registerUser({ email, password, name });
+
+    if (!result.success) {
+      return NextResponse.json({ error: result.error }, { status: 400 });
+    }
+
+    return NextResponse.json({ user: result.user }, { status: 201 });
+  } catch (error) {
+    console.error('Registration error:', error);
+    return NextResponse.json({ error: 'Erreur lors de la création du compte' }, { status: 500 });
+  }
+}
+