refactor: wire web to the in-repo engine and shared data dir

- web/src/server/paths.ts resolves the repo root from its own location,
  loads the single repo-root .env, and defines data/web/ (watchlist,
  stock cache, backtest cache) and data/precomputed/.
- The API spawns bridge.py at the repo root instead of ../quant.
- precompute_backtest.py writes to data/precomputed/ instead of
  ../stock-agent/data/precomputed.
- Rename the project to quant-trading (web package quant-trading-web).

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

.env.example

@@ -0,0 +1,5 @@
+# Copy to .env (untracked) at the repository root.
+# IPADS Responses API key for the web watchlist agent; blank uses demo data.
+IPADS_API_KEY=
+# Proxy URL for the live monitor's market-data fetches (deploy/start-monitor.sh).
+QUANT_MARKET_PROXY=