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, 7 insertions, 1 deletions

diff --git a/src/app/views/ChatPane.svelte b/src/app/views/ChatPane.svelte
index 636cd7c..31e719e 100644
--- a/src/app/views/ChatPane.svelte
+++ b/src/app/views/ChatPane.svelte
@@ -7,13 +7,18 @@
    * preservation, the ScrollToBottom affordance, and the empty-state
    * watermark. Keyed on the active conversation exactly like today's ChatView.
    */
-  import { ChatView } from "../../features/chat";
+  import { ChatView, isClaudeSubscriptionModel } from "../../features/chat";
   import { createSmartScrollController, ScrollToBottom } from "../../features/smart-scroll";
   import { preserveViewportAcross, type AppViewPorts } from "../view-ports";
 
   let { ports }: { ports: AppViewPorts } = $props();
   const store = $derived(ports.store);
 
+  // Cache timer: Claude Code subscription models only (5-minute prompt-cache expiry).
+  const cacheTimer = $derived(
+    isClaudeSubscriptionModel(store.activeModel) ? store.activeChat.cacheTimer : null,
+  );
+
   // One controller owns the chat scroll region; the effects below feed it the
   // edges (identical to the App.svelte wiring this moved out of).
   const smartScroll = createSmartScrollController();
@@ -81,6 +86,7 @@
           thinkingKeyBase={store.activeChat.thinkingKeyBase}
           providerRetry={store.activeChat.providerRetry}
           apiBaseUrl={store.httpBase}
+          {cacheTimer}
         />
       {/key}
     </div>