Finally it works. App Router setup without i18n routing
https://next-intl-docs.vercel.app/docs/getting-started/app-router/without-i18n-routing

middleware.ts

import { NextResponse } from 'next/server';
import type { NextRequest } from 'next/server';

export function middleware(request: NextRequest) {   
  const requestHeaders = new Headers(request.headers);
  const url = new URL(request.url);
  const locale = url.pathname.split('/').filter(Boolean)[1];
  requestHeaders.set('locale', locale);

  const response = NextResponse.next({
    request: {
      headers: requestHeaders,
    },
  });

  return response;
}

i18n/request.ts:

import { getRequestConfig } from 'next-intl/server';
import { headers } from 'next/headers';

export default getRequestConfig(async () => {
  // Provide a static locale, fetch a user setting,
  // read from `cookies()`, `headers()`, etc.

  const locales = ['en', 'de'];
  const headersList = headers();
  const l = headersList.get('locale') || '';
  
  let locale = 'en';
  if (locales.includes(l)) {
    locale = l;
  }

  return {
    locale,
    messages: (await import(`../messages/${locale}.json`)).default,
  };
});

[code]/[locale]/page.tsx

import { useTranslations } from 'next-intl';

export default function HomePage() {
  const t = useTranslations('HomePage');

  return <h1>{t('title')}</h1>;
}

messages/de.json

{
  "HomePage": {
    "title": "Hallo Welt!"
  }
}

messages/en.json

{
  "HomePage": {
    "title": "Hello world!"
  }
}