feat(slice-1): FastAPI factory + /healthz; self-migrate at startup (INV-1/§6.4)

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

backend/tests/test_healthz.py

@@ -0,0 +1,24 @@
+from fastapi.testclient import TestClient
+
+from app.main import create_app
+
+
+def test_healthz_ok_on_migrated_empty_db(fresh_db_url):
+    app = create_app(database_url=fresh_db_url)
+    with TestClient(app) as client:
+        resp = client.get("/healthz")
+    assert resp.status_code == 200
+    assert resp.json() == {"status": "ok"}
+
+
+def test_startup_migrates_from_empty(fresh_db_url):
+    # create_app on an empty DB must self-migrate so /healthz reports current.
+    app = create_app(database_url=fresh_db_url)
+    with TestClient(app) as client:
+        assert client.get("/healthz").status_code == 200
+    # the schema_migrations row exists -> migrations ran at startup
+    import psycopg
+
+    with psycopg.connect(fresh_db_url) as conn:
+        n = conn.execute("SELECT count(*) FROM schema_migrations").fetchone()[0]
+    assert n >= 1