fix: add web search stub and API catch-all for demo deployment

- Add /api/web-search stub returning empty results in demo mode
- Add /aiui/api/* catch-all returning JSON 404 instead of HTML fallback
- Fix nginx proxy to catch all /api/ routes (not just /aiui/api/web-search)

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

neode-ui/docker/nginx-demo.conf

@@ -78,8 +78,8 @@ http {
             }
         }
 
-        # Proxy AIUI API requests (web-search, claude) to backend
-        location /aiui/api/web-search {
+        # Proxy AIUI API requests (web-search, etc.) to backend
+        location /api/ {
             proxy_pass http://neode-backend:5959;
             proxy_http_version 1.1;
             proxy_set_header Host $host;