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/server/src/ws/handler.ts

@@ -415,6 +415,7 @@ class ConnectionManager {
       type: 'space_voice_state',
       spaceId,
       voiceStates: snapshot.voiceStates,
+      voiceRoomStarts: snapshot.voiceRoomStarts,
       voiceUserStates: snapshot.voiceUserStates,
       spaceVoiceStates: snapshot.spaceVoiceStates,
     });
@@ -442,11 +443,13 @@ class ConnectionManager {
    */
   buildSpaceVoiceState(spaceId: string, userId: 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 }>;
   } {
     const db = getDb();
     const voiceStates: Record<string, string[]> = {};
+    const voiceRoomStarts: Record<string, number> = {};
     const voiceUserStates: Record<string, { isMuted: boolean; isDeafened: boolean; isCameraOn: boolean; isScreenSharing: boolean }> = {};
     const spaceVoiceStates: Record<string, { spaceMuted: boolean; spaceDeafened: boolean; permissionMuted: boolean }> = {};
 
@@ -463,6 +466,8 @@ class ConnectionManager {
       if (participants.size > 0) {
         const ids = Array.from(participants);
         voiceStates[ch.id] = ids;
+        const startedAt = this.getRoomStartedAt(ch.id);
+        if (startedAt !== null) voiceRoomStarts[ch.id] = startedAt;
         for (const uid of ids) {
           const status = this.getVoiceUserStatus(uid);
           if (status) voiceUserStates[uid] = status;
@@ -500,7 +505,7 @@ class ConnectionManager {
       }
     }
 
-    return { voiceStates, voiceUserStates, spaceVoiceStates };
+    return { voiceStates, voiceRoomStarts, voiceUserStates, spaceVoiceStates };
   }
 
   // ─── Unified VoiceRoom API ─────────────────────────────────────────────────
@@ -976,6 +981,30 @@ class ConnectionManager {
     }
   }
 
+  /**
+   * When the current occupancy of a room began. Null when nobody is in it —
+   * empty space rooms are destroyed, which is what makes the call timer reset
+   * once the last person leaves.
+   */
+  getRoomStartedAt(roomId: string): number | null {
+    return this.voiceRooms.get(roomId)?.startedAt ?? null;
+  }
+
+  /**
+   * Send only to the people actually inside a room.
+   *
+   * Distinct from `sendToRoom`, which fans a space room out to the whole
+   * space — right for presence updates the sidebar shows, wrong for anything
+   * audible: a soundboard clip must reach the call, not everyone online.
+   */
+  sendToRoomParticipants(roomId: string, event: ServerEvent): void {
+    const room = this.voiceRooms.get(roomId);
+    if (!room) return;
+    for (const userId of room.participants) {
+      this.sendToUser(userId, event);
+    }
+  }
+
   /** Send to all connections of all online users. */
   sendToAll(event: ServerEvent, excludeUserId?: string): void {
     const message = JSON.stringify(event);