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/audio/AudioManager.ts

@@ -185,6 +185,34 @@ export class AudioManager {
     }
   }
 
+  /**
+   * Plays a sound from an arbitrary URL (soundboard clips, which live in the
+   * upload directory rather than /sounds). Cached by URL like the built-in
+   * effects, so repeats do not re-download.
+   */
+  async playUrl(url: string, options: { volume?: number } = {}): Promise<void> {
+    try {
+      const ctx = this.ensureContext();
+      await this.resumeContext();
+      let buffer = this.soundBuffers.get(url);
+      if (!buffer) {
+        const response = await fetch(url);
+        if (!response.ok) return;
+        buffer = await ctx.decodeAudioData(await response.arrayBuffer());
+        this.soundBuffers.set(url, buffer);
+      }
+      const source = ctx.createBufferSource();
+      source.buffer = buffer;
+      const gain = ctx.createGain();
+      gain.gain.value = options.volume ?? 1;
+      source.connect(gain);
+      gain.connect(this.getMasterOutput());
+      source.start(0);
+    } catch (err) {
+      console.warn('[AudioManager] playUrl failed', err);
+    }
+  }
+
   async playSound(name: string, options: { loop?: boolean; volume?: number } = {}): Promise<AudioBufferSourceNode | null> {
     await this.resumeContext();
     const buffer = await this.loadSound(name);