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/utils/voiceStateSync.ts

@@ -9,6 +9,7 @@ import { useVoiceStore } from '../stores/voiceStore';
 export interface SpaceVoiceStateSnapshot {
   spaceId: string;
   voiceStates: Record<string, string[]>;
+  voiceRoomStarts?: Record<string, number>;
   voiceUserStates: Record<string, { isMuted: boolean; isDeafened: boolean; isCameraOn: boolean; isScreenSharing: boolean }>;
   spaceVoiceStates: Record<string, { spaceMuted: boolean; spaceDeafened: boolean; permissionMuted: boolean }>;
 }
@@ -33,6 +34,12 @@ export function applySpaceVoiceState(snapshot: SpaceVoiceStateSnapshot): void {
   for (const [channelId, userIds] of Object.entries(snapshot.voiceStates)) {
     setVoiceUsers(channelId, userIds);
   }
+  if (snapshot.voiceRoomStarts) {
+    const { setVoiceRoomStart } = useVoiceStore.getState();
+    for (const [channelId, startedAt] of Object.entries(snapshot.voiceRoomStarts)) {
+      setVoiceRoomStart(channelId, startedAt);
+    }
+  }
   for (const [userId, status] of Object.entries(snapshot.voiceUserStates)) {
     setVoiceUserStatus(userId, status.isMuted, status.isDeafened, status.isCameraOn, status.isScreenSharing);
   }