Replace react-intl with next-intl and consolidate lang files.

Migrate i18n from react-intl to next-intl, eliminating the formatjs
compilation pipeline. Translation files now live as nested JSON in
public/intl/messages/ (single source of truth), removing the duplicated
src/lang/ directory and the copy/compile build steps. The useMessages()
hook API is preserved so all 195+ consumer components are unchanged.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

next.config.ts

@@ -1,6 +1,9 @@
 import 'dotenv/config';
+import createNextIntlPlugin from 'next-intl/plugin';
 import pkg from './package.json' with { type: 'json' };
 
+const withNextIntl = createNextIntlPlugin('./src/i18n/request.ts');
+
 const TRACKER_SCRIPT = '/script.js';
 
 const basePath = process.env.BASE_PATH || '';
@@ -164,7 +167,7 @@ if (cloudMode) {
 }
 
 /** @type {import('next').NextConfig} */
-export default {
+export default withNextIntl({
   reactStrictMode: false,
   env: {
     basePath,
@@ -202,4 +205,4 @@ export default {
   async redirects() {
     return [...redirects];
   },
-};
+});