refactor: expose aux timer names via runtime store, index in automations

Addresses review feedback on the aux timer naming feature:

- Automation action labels now reference the timers by index
  ("Aux timer 1: start") rather than the custom names, keeping the
  automation config stable regardless of naming.
- Expose the custom names through the consumer-facing runtime interface:
  the aux timer objects broadcast over the websocket now carry a `name`
  field. Names are seeded from the persisted settings at bootstrap and
  kept in sync whenever the settings change, so every consumer (views and
  integrations) reads them from the same runtime data.
- The client control and view consumers now read the name from the
  runtime store instead of querying settings directly; the settings form
  remains the persisted editing source.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WCZejVTzuAY3tHTE6nB3JH

apps/client/src/views/studio/Studio.tsx

@@ -49,7 +49,7 @@ function Studio({ customFields, projectData, isMirrored, settings, viewSettings
 
       <div className={cx(['studio-contents', hideCards && 'studio-contents--onecol'])}>
         <StudioClock hideCards={hideCards} />
-        {!hideCards && <StudioTimers viewSettings={viewSettings} auxTimerNames={settings?.auxTimerNames} />}
+        {!hideCards && <StudioTimers viewSettings={viewSettings} />}
       </div>
     </div>
   );