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>

packages/db/src/index.ts

@@ -1,4 +1,4 @@
-export { prisma } from './client.js';
+export { prisma } from './client';
 export {
   ActivityLevel,
   CookingTime,

packages/db/tsconfig.json

@@ -1,9 +1,10 @@
 {
-  "extends": "@ketopath/tsconfig/node.json",
+  "extends": "@ketopath/tsconfig/base.json",
   "compilerOptions": {
     "outDir": "dist",
     "rootDir": "src",
-    "composite": true
+    "composite": true,
+    "types": ["node"]
   },
   "include": ["src/**/*"],
   "exclude": ["node_modules", "dist"]