Bound /readyz so kubelet probes cannot hang the Service

/readyz walked the hash chain and opened pooled connections with no
libpq connect_timeout, so a 2s kubelet probe never saw a response and
the pod stayed unready. Informed Decision accept is blocked on that.

Probe health() only, under a 1.5s budget, publish last-known
tamper_evidence, and fail TCP handshake in 1s. Integrity stays on
/v1/integrity.

Assistant: grok
Assistant-Session: 01a0a182-bab7-7f11-b32b-d06f3af52082

tests/test_integrity.py

@@ -303,6 +303,32 @@ def test_postgres_policy_treats_an_unreadable_attestation_as_absent(tmp_path):
     assert backend.tamper_evidence_state().reason == "no_attestation"
 
 
+def test_postgres_readiness_policy_does_not_walk_the_chain(tmp_path):
+    backend = _bare_postgres_backend(tmp_path)
+
+    def _boom(attestation=None):
+        raise AssertionError("/readyz must not walk the chain")
+
+    backend.verify_chain = _boom
+    policy = backend.readiness_policy()
+    assert policy.tamper_evidence is False
+    assert policy.durable is True
+    assert policy.custody_class == "operational"
+
+
+def test_postgres_readiness_policy_reports_a_cached_claim(tmp_path):
+    from audit_core.integrity import TamperEvidenceState, utc_now
+
+    backend = _bare_postgres_backend(tmp_path)
+    backend.verify_chain = lambda attestation=None: (_ for _ in ()).throw(
+        AssertionError("cached claim must not walk")
+    )
+    backend._tamper_state = TamperEvidenceState(
+        claimed=True, reason="attested", observed_at=utc_now(),
+    )
+    assert backend.readiness_policy().tamper_evidence is True
+
+
 def test_postgres_policy_drops_the_claim_when_the_chain_cannot_be_walked(tmp_path):
     from audit_core.integrity import utc_now