feat(sound): snapshot getter + volume-update event on SoundManager

Extends the snapshot pattern to the three audio volume levels (system /
furni / trax) so volume-slider widgets on the React client can subscribe
to a single source of truth via useSyncExternalStore.

API additions on ISoundManager:
- systemVolume / furniVolume getters (parity with the existing
  traxVolume getter)
- getVolumesSnapshot(): Readonly<ISoundVolumesSnapshot> with the same
  lazy-frozen + invalidation-on-change semantics as the user/session
  snapshots
- new ISoundVolumesSnapshot { system, furni, trax } interface

New event: NitroEventType.SOUND_VOLUMES_UPDATED. Dispatched only when
the incoming NitroSettingsEvent.SETTINGS_UPDATED actually changes one
of the three volumes (a no-op refresh stays quiet).

While in there, fixed a real bug: the previous implementation cached
`volumeFurniUpdated` / `volumeTraxUpdated` BEFORE writing the new
values, but read `castedEvent.volumeFurni` / `castedEvent.volumeTrax`
in their pre-division form — comparing percent (e.g. 75) against the
already-divided stored value (e.g. 0.75) — so the change check almost
always reported "updated" for a real settings push and never reported
"updated" if the percent matched the stored fraction by coincidence
(only 0/100 are stable). Updated check is now consistent (compare
fraction vs fraction) and also tracks systemVolume changes for the
new snapshot invalidation.

packages/api/src/nitro/sound/ISoundManager.ts

@@ -1,8 +1,22 @@
 import { IMusicController } from './IMusicController';
+import { ISoundVolumesSnapshot } from './ISoundVolumesSnapshot';
 
 export interface ISoundManager
 {
     init(): Promise<void>;
     musicController: IMusicController;
     traxVolume: number;
+    systemVolume: number;
+    furniVolume: number;
+
+    /**
+     * Returns a referentially-stable snapshot of the three volume
+     * levels (system / furni / trax). The same reference is returned
+     * across reads until a volume changes; mutations dispatch
+     * `NitroEventType.SOUND_VOLUMES_UPDATED` to signal invalidation.
+     *
+     * Pairs with `useSyncExternalStore` on the React client for
+     * volume-slider widgets.
+     */
+    getVolumesSnapshot(): Readonly<ISoundVolumesSnapshot>;
 }

packages/api/src/nitro/sound/ISoundVolumesSnapshot.ts

@@ -0,0 +1,6 @@
+export interface ISoundVolumesSnapshot
+{
+    system: number;
+    furni: number;
+    trax: number;
+}

packages/api/src/nitro/sound/index.ts

@@ -2,3 +2,4 @@ export * from './IMusicController';
 export * from './IPlaylistController';
 export * from './ISongInfo';
 export * from './ISoundManager';
+export * from './ISoundVolumesSnapshot';