docs(backlog): mark event-store health probe shipped, add QA plan

Flip §A EVENT_STORE probe to pending-live-QA (7a1362c), register the QA gate
in §F, and add docs/qa/QA-event-store-health-probe.md (responsive/HEALTHY,
no-log-pollution, slow/throw DEGRADED, restore hysteresis, replay independence).

BACKLOG.md

@@ -30,7 +30,10 @@ f8fd260) — those are RETRO candidates once live-QA'd. Remaining:
       `GET /health` + tokens/sec degradation watch (windowed avg of recorded `InferenceCompletedEvent`s,
       opt-in via `llama_tps_warn_below`). Plugs into the existing `HealthMonitor`. QA gate in §F →
       `docs/qa/QA-llama-health-probe.md`.
-- [ ] **§4 EVENT_STORE health probe** — append + fsync latency heartbeat.
+- [~] **§4 EVENT_STORE health probe** — **SHIPPED (pending live-QA)** `7a1362c`. Times a cheap
+      `lastGlobalSequence()` read as a responsiveness heartbeat (DEGRADED on throw or over
+      `event_store_latency_warn_ms`); read-only by design (no probe writes into the log). QA gate in §F →
+      `docs/qa/QA-event-store-health-probe.md`.
 - [ ] **§4/§3 live health TUI pane** — deferred to follow the metrics cadence
       (projection + CLI first, then pane). `correx health` CLI already exists.
 - [ ] **§3 tier-2 stats** — full session-completion summary pane polish (basic pane shipped).
@@ -125,6 +128,8 @@ These are SHIPPED in code but prompt-/server-/network-dependent and not yet live
 - [ ] **LLAMA_SERVER health probe live-QA** — `aaf896d`; needs a real llama-server to ping.
       Plan: `docs/qa/QA-llama-health-probe.md` (liveness up/down/restore, non-2xx, tps degrade,
       restart hysteresis, replay independence).
+- [ ] **EVENT_STORE health probe live-QA** — `7a1362c`. Plan: `docs/qa/QA-event-store-health-probe.md`
+      (responsive→HEALTHY, no-log-pollution, slow/throw→DEGRADED, restore hysteresis, replay independence).
 - [ ] **TUI kernel-steering + AMD gauge fresh live-QA** — approve+note actually revising the
       *same* stage's output; AMD VRAM/RAM gauge on the real box.
 - [ ] **Unit-tested-only fixes, not live-verified:** `1a7eb05` (verdict-edge rejection),