feat(auth): add POST /api/auth/register endpoint (task 4.1)

Validates email presence and password length (8+ chars), checks email
uniqueness with 409 on conflict, hashes password with bcryptjs (cost 12),
inserts user into the users table and returns 201 with id/email/name.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

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

@@ -0,0 +1,64 @@
+import { NextRequest, NextResponse } from 'next/server';
+import bcryptjs from 'bcryptjs';
+import { eq } from 'drizzle-orm';
+import { db } from '@/lib/db';
+import { users } from '@/lib/db/schema';
+
+export async function POST(request: NextRequest) {
+  let body: unknown;
+  try {
+    body = await request.json();
+  } catch {
+    return NextResponse.json({ error: 'Invalid JSON body' }, { status: 400 });
+  }
+
+  const { email, password, name } = body as Record<string, unknown>;
+
+  // Validate email
+  if (!email || typeof email !== 'string' || email.trim() === '') {
+    return NextResponse.json({ error: 'Email is required' }, { status: 400 });
+  }
+
+  // Validate password
+  if (!password || typeof password !== 'string' || password.length < 8) {
+    return NextResponse.json(
+      { error: 'Password must be at least 8 characters' },
+      { status: 400 }
+    );
+  }
+
+  const normalizedEmail = email.trim().toLowerCase();
+
+  // Check email uniqueness
+  const [existingUser] = await db
+    .select({ id: users.id })
+    .from(users)
+    .where(eq(users.email, normalizedEmail))
+    .limit(1);
+
+  if (existingUser) {
+    return NextResponse.json(
+      { error: 'An account with this email already exists' },
+      { status: 409 }
+    );
+  }
+
+  // Hash password
+  const password_hash = await bcryptjs.hash(password, 12);
+
+  // Insert user
+  const [newUser] = await db
+    .insert(users)
+    .values({
+      email: normalizedEmail,
+      password_hash,
+      name: typeof name === 'string' && name.trim() !== '' ? name.trim() : null,
+      provider: 'credentials',
+    })
+    .returning({ id: users.id, email: users.email, name: users.name });
+
+  return NextResponse.json(
+    { id: newUser.id, email: newUser.email, name: newUser.name },
+    { status: 201 }
+  );
+}