perf(desktop): faster session resume & warm AudioContext at idle

- Resume: fire the REST transcript prefetch and the session.resume RPC in
  parallel, and skip the redundant message conversion + reconciliation
  when the prefetch already hydrated the transcript.
- Haptics: web-haptics builds its AudioContext lazily on first trigger,
  paying the ~850ms CoreAudio spin-up on the first streamStart haptic as
  the first token paints. Open/close a throwaway context at idle so the
  real one connects to an already-warm audio service.

apps/desktop/src/components/haptics-provider.tsx

@@ -15,5 +15,29 @@ export function HapticsProvider({ children }: { children: ReactNode }) {
     return () => registerHapticTrigger(null)
   }, [muted, trigger])
 
+  // web-haptics builds its AudioContext lazily inside the first trigger(), and
+  // the process's first AudioContext pays the CoreAudio spin-up (~850ms stall
+  // in profiles) — which landed on the first streamStart haptic as the first
+  // token painted. Open/close a throwaway context at idle so the real one
+  // connects to an already-warm audio service in single-digit ms.
+  useEffect(() => {
+    if (typeof requestIdleCallback !== 'function' || typeof AudioContext === 'undefined') {
+      return undefined
+    }
+
+    const id = requestIdleCallback(
+      () => {
+        try {
+          void new AudioContext().close().catch(() => undefined)
+        } catch {
+          // No audio device (headless CI) — nothing to warm.
+        }
+      },
+      { timeout: 2000 }
+    )
+
+    return () => cancelIdleCallback(id)
+  }, [])
+
   return <>{children}</>
 }