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/server/src/services/aux-timer-service/AuxTimerService.ts

@@ -24,6 +24,20 @@ export class AuxTimerService {
     this.getTime = getTime;
   }
 
+  /**
+   * Applies custom names to the aux timers and broadcasts the change.
+   * Names are indexed by aux timer position (0 -> aux1, 1 -> aux2, 2 -> aux3).
+   * Used to seed the names at bootstrap and to keep them in sync with the settings.
+   */
+  loadNames(names: string[]) {
+    const patch: AuxTimerStateUpdate = {
+      auxtimer1: this.aux1.setName(names[0] ?? ''),
+      auxtimer2: this.aux2.setName(names[1] ?? ''),
+      auxtimer3: this.aux3.setName(names[2] ?? ''),
+    };
+    this.emit(patch);
+  }
+
   /**
    * Whether any of the aux timers are currently running
    */