Stop an unreachable database from presenting as Bad Gateway

Two faults compounded into one symptom: with the database unreachable, every
route on the service returned 502 - including /docs, which never touches it.

_connect() passed no connect_timeout. A host that DROPS packets rather than
refusing them, which is what a firewall or a wrong DB_HOST looks like, blocked
until the OS gave up - roughly 130 seconds on Linux. Every caller inherited
that, /api/health included. Now bounded by DB_CONNECT_TIMEOUT_SECONDS,
defaulting to 5. Measured against an unroutable host: /api/health went from
hanging past 25s to answering 200 in 5.07s.

The container healthcheck then probed /api/health, so that hang timed out the
check, the container was marked unhealthy, and the platform stopped routing to
it. That is the part that turned a degraded dependency into a total outage, and
it was introduced with the healthcheck itself.

A healthcheck is a LIVENESS question, because the platform's answer to "no" is
to take the container out of service. It may only ask whether the process is
still serving HTTP. /api/health is a READINESS report - it dials Postgres and
Ollama to say whether they are reachable, and coupling the container's
existence to its dependencies is what made a running API unreachable. It now
probes "/", which is served from memory and does no I/O, so it can fail only if
the app really is gone.

Verified with an unroutable DB host: /, /docs and /openapi.json all answer 200,
and the healthcheck exits 0. With the app stopped it still exits 1.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

app/services/vector_store.py

@@ -7,7 +7,10 @@ import logging
 import re
 import psycopg
 
-from app.infrastructure.settings import DATABASE_URL, USE_PGVECTOR, DB_HOST, DB_PORT, DB_NAME, DB_USER, DB_PASSWORD
+from app.infrastructure.settings import (
+    DATABASE_URL, USE_PGVECTOR, DB_HOST, DB_PORT, DB_NAME, DB_USER, DB_PASSWORD,
+    DB_CONNECT_TIMEOUT_SECONDS,
+)
 from app.services.brand_registry import BRAND_ALIASES, resolve_parent_brand
 
 
@@ -91,7 +94,15 @@ def _connect() -> Optional[psycopg.Connection]:
             dbname=DB_NAME,
             user=DB_USER,
             password=DB_PASSWORD,
-            autocommit=True
+            autocommit=True,
+            # Without this, a host that DROPS packets rather than refusing them
+            # - a firewall, a wrong DB_HOST - blocks here until the OS gives up,
+            # which is around 130 seconds on Linux. Every caller of _connect()
+            # inherits that: /api/health stops answering, the container's
+            # healthcheck times out, and the platform pulls the service out of
+            # its load balancer. "Database unreachable" then presents as a Bad
+            # Gateway on every route, including ones that never touch the DB.
+            connect_timeout=DB_CONNECT_TIMEOUT_SECONDS,
         )
     except Exception as e:
         logger.error(f"Vector DB connection failed: {e}")