feat(phase-0): scaffold backend + web + docker + DB schema

- docker-compose.yml: timescaledb-ha (timescaledb 2.27 + vectorscale + pgvector + pgai)
  + backend (FastAPI, CUDA 12.1) + web (Next.js 14)
- docker-compose.gpu.yml: GPU profile overlay for RTX 3070 Ti
- build.bat: Windows bootstrap, auto-detects nvidia-smi and selects GPU/CPU compose
- backend: Dockerfile, pyproject.toml, FastAPI skeleton with /health and /health/db
- DB migration 001_init.sql: symbols (with trigram search), ohlcv_daily/1m (hypertables),
  macro_daily, trading_value_daily, news (vector embedding), predictions
  (with user_triggered flag for on-demand UX), prediction_outcomes, model_performance
- web: Next.js 14 + Tailwind + lightweight-charts placeholder
- README: KIS/DART/HuggingFace token issuance guides + 10 seed tickers + run instructions

backend/app/db/connection.py

@@ -0,0 +1,30 @@
+from __future__ import annotations
+
+from sqlalchemy import create_engine, text
+from sqlalchemy.engine import Engine
+
+from app.config import settings
+
+
+_engine: Engine | None = None
+
+
+def get_engine() -> Engine:
+    global _engine
+    if _engine is None:
+        _engine = create_engine(settings.database_url, pool_pre_ping=True, future=True)
+    return _engine
+
+
+def ping() -> dict[str, object]:
+    """Smoke-test: DB 연결 + 확장 확인."""
+    eng = get_engine()
+    with eng.connect() as conn:
+        version = conn.execute(text("SELECT version()")).scalar()
+        exts = conn.execute(
+            text(
+                "SELECT extname FROM pg_extension "
+                "WHERE extname IN ('timescaledb','vector','pg_trgm') ORDER BY extname"
+            )
+        ).scalars().all()
+    return {"server": version, "extensions": list(exts)}