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

packages/types/src/definitions/runtime/AuxTimer.type.ts

@@ -14,4 +14,6 @@ export type SimpleTimerState = {
   current: number;
   playback: SimplePlayback;
   direction: SimpleDirection;
+  /** Custom name for the aux timer. Empty string when unnamed */
+  name: string;
 };

packages/types/src/definitions/runtime/RuntimeStore.ts

@@ -53,18 +53,21 @@ export const runtimeStorePlaceholder: Readonly<RuntimeStore> = {
     direction: SimpleDirection.CountUp,
     duration: 0,
     playback: SimplePlayback.Stop,
+    name: '',
   },
   auxtimer2: {
     current: 0,
     direction: SimpleDirection.CountUp,
     duration: 0,
     playback: SimplePlayback.Stop,
+    name: '',
   },
   auxtimer3: {
     current: 0,
     direction: SimpleDirection.CountUp,
     duration: 0,
     playback: SimplePlayback.Stop,
+    name: '',
   },
   ping: 1,
 };