docs(backlog): mark health TUI pane shipped, add QA plan

Flip §A live health TUI pane to pending-live-QA (fd67a6c), register the QA
gate in §F, add docs/qa/QA-health-tui-pane.md. Note that §4 health-checks is
now feature-complete in code (3 probes + pane) — retire as a unit once QA passes.

BACKLOG.md

@@ -34,8 +34,11 @@ f8fd260) — those are RETRO candidates once live-QA'd. Remaining:
       `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.
+- [~] **§4/§3 live health TUI pane** — **SHIPPED (pending live-QA)** `fd67a6c`. `OverlayHealth` (key `H` /
+      palette "health checks") mirrors the stats pane: pull-based fetch over WS
+      (`GetHealthChecks` → `health.checks`/`HealthReport`), per-subject status with degraded loud, visible
+      fallback when disabled. QA gate in §F → `docs/qa/QA-health-tui-pane.md`. **With all three probes +
+      this pane, §4 health-checks is feature-complete in code** — retire as a unit once the QA gates pass.
 - [ ] **§3 tier-2 stats** — full session-completion summary pane polish (basic pane shipped).
 - 🚫 **§3 tier-3 Prometheus/Grafana export** — spec says "deferred indefinitely". **Do not build.**
 
@@ -130,6 +133,8 @@ These are SHIPPED in code but prompt-/server-/network-dependent and not yet live
       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).
+- [ ] **Health TUI pane live-QA** — `fd67a6c`. Plan: `docs/qa/QA-health-tui-pane.md` (`H` opens/fetches,
+      matches `correx health`, degraded loud, disabled fallback, resize, live wire-contract values).
 - [ ] **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),