implement better-auth auth with postgres and route protection

app/api/auth/[...all]/route.ts

@@ -0,0 +1,9 @@
+import { toNextJsHandler } from 'better-auth/next-js';
+import { ensureAuthSchema } from '@/lib/auth';
+
+const authHandler = toNextJsHandler(async (request: Request) => {
+  const auth = await ensureAuthSchema();
+  return auth.handler(request);
+});
+
+export const { GET, POST, PATCH, PUT, DELETE } = authHandler;