feat(metrics): inline cache hit-rate badges (last turn + chat total)

Derive cache hit rate (cacheReadTokens / inputTokens) from data already
folded in core/metrics — no backend/contract change.

- core/metrics: computeCachePct + viewCacheRate (pct + success/warning/error
  level by 66/33 thresholds + isHit); thread a running cumulativeUsage onto
  each finalized turn-metrics row for the conversation total.
- ChatView: render two labelled, colour-coded percentage badges in the
  turn-total bubble — "Last turn:" (that turn) and "Chat Total:" (cumulative).
- Honour backend caveats: absent cache fields -> 0, divide-by-zero guarded,
  a legitimate 0% renders plainly (not "no data").

1 files changed, 27 insertions, 1 deletions

diff --git a/src/core/metrics/format.ts b/src/core/metrics/format.ts
index 3a4078c..cc86976 100644
--- a/src/core/metrics/format.ts
+++ b/src/core/metrics/format.ts
@@ -1,5 +1,5 @@
 import type { StepMetrics, TurnMetrics, Usage } from "@dispatch/wire";
-import type { StepMetricsView, TurnMetricsView } from "./types";
+import type { CacheRateView, StepMetricsView, TurnMetricsView } from "./types";
 
 function formatTokens(n: number): string {
 	return n.toLocaleString("en-US");
@@ -49,6 +49,32 @@ export function viewStepMetrics(step: StepMetrics, index: number): StepMetricsVi
 	};
 }
 
+/**
+ * Cache hit rate as a 0..100 integer percentage: `cacheReadTokens / inputTokens`,
+ * clamped to [0,1]. Absent cache field counts as 0; a 0% rate is legitimate (not
+ * missing data). Returns 0 when there are no input tokens.
+ */
+export function computeCachePct(u: Usage): number {
+	const read = u.cacheReadTokens ?? 0;
+	if (u.inputTokens <= 0) return 0;
+	const rate = read / u.inputTokens;
+	const clamped = rate < 0 ? 0 : rate > 1 ? 1 : rate;
+	return Math.round(clamped * 100);
+}
+
+/** Colour severity for a cache hit percentage (badge colour). */
+function cacheLevel(pct: number): "success" | "warning" | "error" {
+	if (pct >= 66) return "success";
+	if (pct >= 33) return "warning";
+	return "error";
+}
+
+/** Build a view of a cache hit rate (percentage + colour level + hit flag). */
+export function viewCacheRate(u: Usage): CacheRateView {
+	const pct = computeCachePct(u);
+	return { pct, level: cacheLevel(pct), isHit: (u.cacheReadTokens ?? 0) > 0 };
+}
+
 /** Build a formatted view of a turn's aggregate metrics. */
 export function viewTurnMetrics(turn: TurnMetrics): TurnMetricsView {
 	const total = totalTokens(turn.usage);