feat: orchestrator Agent mode UI + claude_allow_dir tool + fix DDG search

- Add Agent mode toggle to web UI input row — routes through POST /orchestrate
  instead of /chat; polls for result with live tool-call count in thinking bubble
- Add cortex/tools/system.py with claude_allow_dir tool; registers in tool registry
- Fix web search: duckduckgo_search renamed to ddgs, update import + requirements.txt
- Allow WebSearch and WebFetch in ~/.claude/settings.json for Claude CLI fallback
- Add claude-allow-dir script docs and security note to CLAUDE.md

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

cortex/static/index.html

@@ -137,6 +137,7 @@
             <!-- Note mode controls -->
             <button id="note-type-btn">private</button>
             <button id="note-btn">Note</button>
+            <button id="agent-mode-btn" title="Agent mode — Gemini tool loop + Claude response">Agent</button>
             <button id="send">Send</button>
             <button id="stop">Stop</button>
         </div>