Headroom proxy integration with AI session summaries and spend analytics

[akhilsinghcodes]

Summary

• Headroom proxy routing: Added [headroom-shell] and [headroom-chat] session types that route Claude CLI and LiteLLM chat through the local Headroom context-compression proxy at http://localhost:8787
• Token tracking fix: Fixed applyUsageTick guard to correctly strip the [headroom-shell]: command prefix before comparing, so in/out/cost stats are correctly tracked for headroom-shell sessions
• AI session summaries: Added POST /api/sessions/:id/summary endpoint that calls gpt-4o-mini via LiteLLM to generate a title + 2–3 sentence summary; persisted as a session_summary artifact and surfaced as session_title in the session list sidebar
• Headroom Spend Analytics tab: Replaced static Headroom card with a live iframe of the Headroom dashboard (/dashboard) plus a "Request Log" subtab that reads per-request data from data/headroom-requests.jsonl (written via --log-file flag)
• Dev script fixes: Added port-kill-before-start for port 8787, suppressed PyTorch/tokenizer warnings, added --memory flag to enable cross-session context persistence, added inline torch install check with pip cache (non-blocking)
• Session sidebar search: Added search box to filter sessions by command or title
• Dashboard date/SQL fixes: UTC week alignment for date presets, AND command NOT IN ('zsh', 'bash') filter on all spend queries to exclude raw shell sessions
• Docs: Added HEADROOM.md with setup guide and screenshots; updated README.md with all new features and 7 new screenshots

Test plan

• Start dev with pnpm dev:one, confirm Headroom proxy launches on port 8787 without conflict
• Create a [headroom-shell] session running claude, verify in/out/cost tokens update in real time
• Open Spend Analytics → Headroom tab, confirm iframe loads and Request Log table populates after a few requests
• Open any completed session → Artifacts → Generate Summary, verify title appears in sidebar
• Restart the server, confirm Headroom dashboard retains lifetime stats from ~/.headroom/proxy_savings.json
• Verify zsh/bash sessions are excluded from all spend analytics queries