feat(web): integrate Better Auth with sign-in/sign-up pages

Web app integration:
- /api/auth/[...all] route exposes Better Auth handler
- src/lib/auth.ts: server helper getServerSession() reading cookies via headers()
- src/lib/auth-client.ts: browser auth client built on shared makeAuthClient
- (auth) route group with sign-in and sign-up pages, both with email+password
  form and "Continua con Google" button (Google flow active when env is set)
- Home page becomes async, shows signed-in user name with sign-out button or
  routes to sign-up/sign-in CTAs
- Italian copy in messages/it.json under Auth.SignIn / Auth.SignUp
- transpilePackages includes @ketopath/auth
- .env.example: BETTER_AUTH_SECRET, BETTER_AUTH_URL, DATABASE_URL, Google placeholders

Build tooling:
- Drop .js extensions from internal package imports so Next webpack can
  transpile them; switch packages/db tsconfig from NodeNext to Bundler
  resolution to keep TS happy (same as packages/auth)

Verified end-to-end via browser:
- /sign-up creates user (Postgres rows in users + accounts), session cookie set,
  redirect to / shows "Accesso effettuato come Mario Test"
- /sign-out clears session, page falls back to anonymous CTAs
- /sign-in with the same credentials restores session

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/web/src/app/[locale]/sign-out-button.tsx

@@ -0,0 +1,29 @@
+'use client';
+
+import { useRouter } from 'next/navigation';
+import { useState } from 'react';
+
+import { authClient } from '@/lib/auth-client';
+
+export function SignOutButton({ label }: { label: string }) {
+  const router = useRouter();
+  const [pending, setPending] = useState(false);
+
+  async function handleClick() {
+    setPending(true);
+    await authClient.signOut();
+    router.push('/');
+    router.refresh();
+  }
+
+  return (
+    <button
+      type="button"
+      onClick={handleClick}
+      disabled={pending}
+      className="rounded-md border border-slate-300 bg-white px-3 py-1.5 text-xs font-medium text-slate-700 shadow-sm hover:bg-slate-50 disabled:opacity-60"
+    >
+      {label}
+    </button>
+  );
+}