feat: soundboard, account menu, and call timer

Soundboard: the trigger travels over the WebSocket and every client in the
call plays the clip locally, instead of mixing it into the presser's
microphone or publishing a LiveKit track. No upstream bandwidth, no media
stack changes, and the clip is not degraded by voice processing.

Fan-out uses a new sendToRoomParticipants rather than sendToRoom: the latter
broadcasts a space room to the whole space, which is right for the presence
the sidebar shows and wrong for anything audible. The cooldown is enforced
server-side — a client-side one only slows down people not trying to abuse it,
and a soundboard is the easiest thing here to turn into a weapon. Playing is
open to anyone in the call; deciding what the buttons are needs MANAGE_SPACE.

Account menu: the name in the user bar had cursor-pointer and no handler, so
the interface was already promising a click that did nothing. Offers profile,
status and copy-id — not the Clips or account switching the reference design
shows, which would be dead UI here.

Call timer: startedAt comes from the server, so a late joiner sees the call's
age rather than their own arrival. Empty space rooms are destroyed already,
which is what makes the next call start from zero — no reset logic needed.

packages/web/src/api/client.ts

@@ -75,6 +75,15 @@ import type {
 } from '@backspace/shared';
 import type { AuditEvent } from '@backspace/shared/src/audit.js';
 
+export interface SoundboardSound {
+  id: string;
+  spaceId: string;
+  name: string;
+  filename: string;
+  uploaderId: string | null;
+  createdAt: number;
+}
+
 export interface StatsLeader {
   userId: string;
   username: string;
@@ -302,6 +311,12 @@ export class BackspaceApiClient {
     removeFavorite: (id: string) => Promise<void>;
   };
 
+  readonly soundboard: {
+    list: (spaceId: string) => Promise<{ sounds: SoundboardSound[] }>;
+    add: (spaceId: string, name: string, filename: string) => Promise<SoundboardSound>;
+    remove: (soundId: string) => Promise<void>;
+  };
+
   readonly stats: {
     space: (spaceId: string, days: number) => Promise<SpaceStats>;
   };
@@ -724,6 +739,13 @@ export class BackspaceApiClient {
       },
     };
 
+    this.soundboard = {
+      list: (spaceId: string) => request<{ sounds: SoundboardSound[] }>('GET', `/spaces/${spaceId}/sounds`),
+      add: (spaceId: string, name: string, filename: string) =>
+        request<SoundboardSound>('POST', `/spaces/${spaceId}/sounds`, { name, filename }),
+      remove: (soundId: string) => request<void>('DELETE', `/sounds/${soundId}`),
+    };
+
     this.stats = {
       space: (spaceId: string, days: number) =>
         request<SpaceStats>('GET', `/spaces/${spaceId}/stats?days=${days}`),