feat(frontend): add next-intl bilingual i18n for core paths

Wire next-intl without locale routes, add zh-CN/en catalogs, language
switcher, and migrate layout/auth/settings UI copy. Document i18n rules
in AGENTS.md and keep static export builds working.

frontend/scripts/check-i18n-keys.mjs

@@ -0,0 +1,35 @@
+import { readFileSync } from 'node:fs';
+import { resolve, dirname } from 'node:path';
+import { fileURLToPath } from 'node:url';
+
+const root = resolve(dirname(fileURLToPath(import.meta.url)), '..');
+
+function flatten(obj, prefix = '') {
+  const keys = new Set();
+  for (const [key, value] of Object.entries(obj)) {
+    const path = prefix ? `${prefix}.${key}` : key;
+    if (value && typeof value === 'object' && !Array.isArray(value)) {
+      for (const child of flatten(value, path)) keys.add(child);
+    } else {
+      keys.add(path);
+    }
+  }
+  return keys;
+}
+
+const zh = JSON.parse(readFileSync(resolve(root, 'messages/zh-CN.json'), 'utf8'));
+const en = JSON.parse(readFileSync(resolve(root, 'messages/en.json'), 'utf8'));
+const zhKeys = flatten(zh);
+const enKeys = flatten(en);
+const onlyZh = [...zhKeys].filter((k) => !enKeys.has(k)).sort();
+const onlyEn = [...enKeys].filter((k) => !enKeys.has(k) === false && !zhKeys.has(k)).sort();
+const onlyEnFixed = [...enKeys].filter((k) => !zhKeys.has(k)).sort();
+
+if (onlyZh.length || onlyEnFixed.length) {
+  console.error('i18n key mismatch');
+  if (onlyZh.length) console.error('only in zh-CN:', onlyZh);
+  if (onlyEnFixed.length) console.error('only in en:', onlyEnFixed);
+  process.exit(1);
+}
+
+console.log(`i18n keys OK (${zhKeys.size} keys)`);