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>

.gitignore

@@ -55,3 +55,7 @@ data/*_unavailable.json
 logs/
 memory/
 .tmp_finance/
+
+# Web UI state and precomputed backtests (web/src/server/paths.ts)
+data/web/
+data/precomputed/