feat(lotus): report remote screenshare audio to the host (cinny #277)

New fromWidget action io.lotus.screenshare_audio_state { present }: each
LivekitRoomAudioRenderer reports whether a remote participant's
ScreenShareAudio track is being received; the combined answer is sent to
the host on change, and cleared when a renderer unmounts. cinny uses it to
show "Mute Screenshare Audio" only when there is something to mute.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_017PCb59uY3UKqDqt7B6hzd5

src/lotus/lotusScreenshareAudio.ts

@@ -8,6 +8,8 @@ Please see LICENSE in the repository root for full details.
 import { BehaviorSubject } from "rxjs";
 
 import { globalScope } from "../state/ObservableScope";
+import { LotusWidgetActions } from "./lotusActions";
+import { lotusSendToHost } from "./lotusWidget";
 
 /**
  * Whether the host has muted remote screenshare AUDIO (`io.lotus.set_deafen`
@@ -25,3 +27,40 @@ export const setScreenshareAudioMuted$ = new BehaviorSubject(false);
 export const muteScreenshareAudio$ = globalScope.behavior(
   setScreenshareAudioMuted$,
 );
+
+/**
+ * [cinny #277] Whether any remote participant's screenshare AUDIO is being
+ * received, so the host shows its "Mute Screenshare Audio" control only when
+ * there is something to mute. Each `LivekitRoomAudioRenderer` (one per SFU)
+ * reports for its own room; the host gets `io.lotus.screenshare_audio_state
+ * { present }` whenever the combined answer changes.
+ */
+const presentByRoom = new Map<string, boolean>();
+let lastSent: boolean | undefined;
+
+function sendIfChanged(): void {
+  const present = [...presentByRoom.values()].some(Boolean);
+  if (present === lastSent) return;
+  lastSent = present;
+  lotusSendToHost(LotusWidgetActions.ScreenshareAudioState, { present });
+}
+
+export function reportScreenshareAudio(
+  roomKey: string,
+  present: boolean,
+): void {
+  presentByRoom.set(roomKey, present);
+  sendIfChanged();
+}
+
+/** The renderer for `roomKey` went away (call left, SFU switched). */
+export function clearScreenshareAudio(roomKey: string): void {
+  presentByRoom.delete(roomKey);
+  sendIfChanged();
+}
+
+/** Test-only: forget all reports. */
+export function resetScreenshareAudioPresence(): void {
+  presentByRoom.clear();
+  lastSent = undefined;
+}