feat: scaffold Brain of Reese — FastAPI RAG chat over Postgres 17 + pgvector

Foundation (phase 01, verified):
- FastAPI app: /api/health, /api/suggestions, /api/chat (placeholder),
  static frontend served locally (no CDN)
- Postgres 17 + pgvector via db/Containerfile + compose.yaml
  (podman compose up -d db), Alembic initial migration (documents,
  chunks with vector(768), query_log)
- LLM client targeting https://aipi.reeseapps.com/v1 (turbo/embed);
  scripts/llm_probe.py verified models + 768-dim embeddings live
- Conditional debugpy: imported only when DEBUGPY=1 (attach on demand,
  :5678); logging config for clean single-line logs
- Frontend shell: mobile-first chat + Sources pages, tokens, a11y baselines
- Tests: 24 unit+integration (99% coverage on app/), ruff + pyright clean,
  Playwright smoke E2E (3 tests) against a deterministic mock LLM
- Planning: .agent/PLAN.md (architecture + LOCKED decisions), AGENTS.md,
  6 user stories, 7 phase files (one story / one phase / one Playwright
  suite each)

tests/unit/test_db.py

@@ -0,0 +1,56 @@
+"""Unit tests: engine/session helpers (no live database required).
+
+Creating a SQLAlchemy engine/session is lazy — no connection opens until the
+first query — so these run anywhere.
+"""
+from __future__ import annotations
+
+from sqlalchemy import Engine
+from sqlalchemy.orm import Session
+
+from app import db as app_db
+
+
+def test_engine_and_session_factory_are_lazy() -> None:
+    assert isinstance(app_db.engine, Engine)
+    session = app_db.SessionLocal()
+    try:
+        assert isinstance(session, Session)
+    finally:
+        session.close()
+
+
+def test_get_db_yields_session_and_closes_generator() -> None:
+    gen = app_db.get_db()
+    session = next(gen)
+    assert isinstance(session, Session)
+    session.close()
+    gen.close()  # exercises the finally: db.close()
+
+
+def test_db_available_true_on_select_one(monkeypatch) -> None:
+    class _FakeConn:
+        def __enter__(self):
+            return self
+
+        def __exit__(self, *exc: object) -> None:
+            return None
+
+        def execute(self, _stmt: object) -> None:
+            return None
+
+    class _FakeEngine:
+        def connect(self) -> _FakeConn:
+            return _FakeConn()
+
+    monkeypatch.setattr(app_db, "engine", _FakeEngine())
+    assert app_db.db_available() is True
+
+
+def test_db_available_false_on_error(monkeypatch) -> None:
+    class _BrokenEngine:
+        def connect(self) -> object:
+            raise ConnectionError("db is down")
+
+    monkeypatch.setattr(app_db, "engine", _BrokenEngine())
+    assert app_db.db_available() is False