Auth.jsのv5-betaと、next-intlを組み合わせてmiddlewareを書く方法が載ってなかったのでメモを残します。

import { auth } from '@/auth';
import { routing } from '@/i18n/routing';
import createMiddleware from 'next-intl/middleware';

const handleI18nRouting = createMiddleware(routing);
export default auth(handleI18nRouting);

export const config = {
  matcher: ['/((?!api|_next|.*\\..*).*)'],
};

なお、authは以下。詳しい書き方はこちら。

export const { handlers, signIn, signOut, auth } = NextAuth({
  // ...
});

また、routingは以下。詳しい書き方はこちら

import { createNavigation } from 'next-intl/navigation';
import { defineRouting } from 'next-intl/routing';

export const routing = defineRouting({
  // A list of all locales that are supported
  locales: ['en', 'ja'],
  // Used when no locale matches
  defaultLocale: 'ja',
});

export type Locale = (typeof routing.locales)[number];

// Lightweight wrappers around Next.js' navigation APIs
// that will consider the routing configuration
export const { Link, redirect, usePathname, useRouter, getPathname } =
  createNavigation(routing);