Remove duplicate FAQ from footer, show New Search only after generation

- FAQ button now only in hero header (removed from footer)
- New Search button hidden by default, shown only after generating

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

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

index.html

@@ -1242,8 +1242,7 @@
     </div>
 
     <div class="footer">
-        <button id="faqBtnFooter" class="faq-link" type="button">FAQ</button>
-        <button id="newSearchBtn" class="faq-link" type="button">New search</button>
+        <button id="newSearchBtn" class="faq-link" type="button" style="display:none;">New search</button>
     </div>
 
     <div class="version-history">