feat(chat): cache timer for Claude Code subscription models

Per-step and per-turn timers for the gaps between model requests (the
Claude prompt cache expires after 5 min idle). A step gap runs live under
the executing tools from step-complete until its last tool result (or the
next step's output), then is stamped on that step's metrics line beside
its cache badge. A turn gap runs live on the turn's metrics line from
done/error until the next message is sent, then is stamped there. Counts
m:ss up to 10 min, then '10+ min'; colour tracks the 5-min TTL.

Gated on claude/<model>. Pure reducer in core/metrics/cache-timer.ts;
the turn gap is seeded from an idle conversation's lastActivityAt so it
survives a reload. Stamps are in-memory only.

1 files changed, 58 insertions, 0 deletions

diff --git a/src/features/chat/ui/CacheTimerBadge.svelte b/src/features/chat/ui/CacheTimerBadge.svelte
new file mode 100644
index 0000000..e5abed5
--- /dev/null
+++ b/src/features/chat/ui/CacheTimerBadge.svelte
@@ -0,0 +1,58 @@
+<script lang="ts">
+  /**
+   * One cache-timer badge. LIVE when given `since` (counts up from that epoch
+   * ms, ticking once a second, and stops ticking at the 10-minute cap); STAMPED
+   * when given `elapsedMs` (a finished gap — static). Formatting lives in
+   * `core/metrics` (`viewCacheTimer`). Owning the tick here means only this
+   * badge re-renders each second, not the transcript.
+   */
+  import { untrack } from "svelte";
+  import { CACHE_TIMER_MAX_MS, viewCacheTimer } from "../../../core/metrics";
+
+  let {
+    since,
+    elapsedMs,
+    now = Date.now,
+  }: {
+    /** Live: epoch ms the gap started. */
+    since?: number;
+    /** Stamped: the gap's final duration (wins over `since`). */
+    elapsedMs?: number;
+    /** Wall clock (injected for tests). */
+    now?: () => number;
+  } = $props();
+
+  // Initial read only (the effect below keeps it current while live).
+  let current = $state(untrack(() => now()));
+
+  $effect(() => {
+    if (elapsedMs !== undefined || since === undefined) return;
+    const start = since;
+    current = now();
+    if (current - start >= CACHE_TIMER_MAX_MS) return;
+    const id = setInterval(() => {
+      current = now();
+      if (current - start >= CACHE_TIMER_MAX_MS) clearInterval(id);
+    }, 1000);
+    return () => clearInterval(id);
+  });
+
+  const badgeClass = {
+    success: "badge-success",
+    warning: "badge-warning",
+    error: "badge-error",
+  } as const;
+
+  const live = $derived(elapsedMs === undefined);
+  const view = $derived(viewCacheTimer(elapsedMs ?? current - (since ?? current)));
+</script>
+
+<span
+  class="badge badge-sm gap-1 font-mono tabular-nums {badgeClass[view.level]}"
+  class:badge-outline={!live}
+  title={live
+    ? "Cache timer (running): time since the last model request. The Claude prompt cache expires after 5 minutes idle."
+    : "Cache timer (stopped): how long the cache sat idle before the next request. The Claude prompt cache expires after 5 minutes idle."}
+  data-testid={live ? "cache-timer-live" : "cache-timer-stamp"}
+  ><span aria-hidden="true">⏱</span>{view.label}</span
+>