fix(docs): complete language switching - update sidebar and hero instantly

Fixed remaining language persistence issues where sidebar and hero section
did not update when switching languages via navbar flags.

**Changes:**
- languageChanged event now calls updatePageUI() to update hero section
- languageChanged event now calls loadDocuments() to reload sidebar
- All UI elements update immediately without requiring page refresh

**Updated Elements on Language Change:**
- Hero section (page title, subtitle, search button)
- Sidebar category labels (Getting Started, Resources, etc.)
- Sidebar document titles (shows translations if available)
- Document content (reloads in new language)
- GitHub section links

**Result:**
✅ Click language flag → entire page switches instantly
✅ No page refresh required
✅ All UI elements synchronized
✅ Ready for Caixin Global launch (Oct 29)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

public/js/docs-app.js

@@ -232,13 +232,22 @@ function updateURL(slug, lang) {
 
 // Listen for language changes from i18n system
 if (typeof window !== 'undefined') {
-  window.addEventListener('languageChanged', (e) => {
+  window.addEventListener('languageChanged', async (e) => {
     const newLang = e.detail.language;
     currentLanguage = newLang;
 
-    // Reload current document in new language
-    if (currentDocument) {
-      loadDocument(currentDocument.slug, newLang);
+    // Update page UI (hero section, sidebar headings, etc.)
+    updatePageUI(newLang);
+
+    // Remember current document slug before reloading list
+    const currentSlug = currentDocument ? currentDocument.slug : null;
+
+    // Reload document list to show translated category labels and document titles
+    await loadDocuments();
+
+    // Reload current document in new language if one was loaded
+    if (currentSlug) {
+      loadDocument(currentSlug, newLang);
     }
   });