feat(apple): screen-audio sharing -- macOS ScreenCaptureKit, iOS ReplayKit

Implement system/desktop audio sharing on the Apple clients, feeding the
existing SCREEN_AUDIO Opus -> AEAD -> UDP path via vc_stream_feed_pcm. No
C++/protocol/codec changes -- the core was already ready (the Windows-only
loopback is #ifdef VOICECAT_HAS_LOOPBACK; off Windows the stream just waits
for fed PCM). Audio only; video is dropped.

macOS (in-process):
- ScreenAudioCapture.swift drives an audio-only SCStream
  (excludesCurrentProcessAudio), converts Float32 -> int16 in the channel's
  mono/stereo mode, and calls feedPcm. Capture starts on the self
  .streamStarted event (effective config known then). Wired into
  MainWindowController.screenAudioClicked().

iOS (forward-to-host, single session):
- VoiceCatBroadcast: a ReplayKit Broadcast Upload Extension consumes
  .audioApp only, resamples to 48kHz int16 stereo (AVAudioConverter), and
  writes a shared App Group SPSC ring (BroadcastAudioRing.swift). It does
  not link libvoicecat.
- Host BroadcastAudioPump drains the ring (reacting to the extension's
  Darwin notifications) and feeds the SCREEN_AUDIO stream it owns, downmixing
  to mono when the channel is mono. Screen audio appears as a second stream
  of the same user; no credentials persisted. UI is RPSystemBroadcastPicker
  View in VoiceControlsView. Removes the speculative BroadcastCredentials.

Docs: voice.md s9, CLAUDE.md status, PROGRESS.md.

clients/apple/macOS/VoiceCatMac/Windows/MainWindowController.swift

@@ -30,6 +30,7 @@ final class MainWindowController: NSWindowController, NSWindowDelegate {
                                              canMoveUsers: false, canAdminAccounts: false, isAdmin: false)
     internal var micStreamId: UInt32 = 0
     private var screenStreamId: UInt32 = 0
+    private var screenCapture: ScreenAudioCapture?
     internal var pttKeyCode: UInt16 = 0x60  // F8
     private var pttMonitor: Any?
     private var serverMuted = false
@@ -477,6 +478,10 @@ final class MainWindowController: NSWindowController, NSWindowDelegate {
             }
 
         case .streamStarted:
+            // Our own SCREEN_AUDIO stream is now live on the server — begin capture.
+            if event.userId == selfUserId && event.streamId == screenStreamId {
+                startScreenCapture()
+            }
             guard let u = users[event.userId], u.channelId == currentChannelId else { break }
             let streams = client.listUserStreams(event.userId)
             let kind = streams.first(where: { $0.id == event.streamId })?.kind
@@ -601,6 +606,7 @@ final class MainWindowController: NSWindowController, NSWindowDelegate {
         channelTree = []; channelOutlineView.reloadData()
         displayedUsers = []; userTableView.reloadData()
         users.removeAll(); talkingUsers.removeAll()
+        stopScreenCapture()
         currentChannelId = 0; micStreamId = 0; screenStreamId = 0
         composeField.isEnabled = false; sendButton.isEnabled = false
         joinVoiceButton?.isEnabled = false
@@ -708,26 +714,70 @@ final class MainWindowController: NSWindowController, NSWindowDelegate {
 
     @objc private func screenAudioClicked() {
         if screenStreamId == 0 {
+            // Announce the stream now; ScreenCaptureKit capture starts once the server's
+            // StreamAnnounceResult lands (the .streamStarted event), when the effective audio
+            // config — and thus the channel count to capture — is known. See startScreenCapture.
             let (result, streamId) = client.startStream(StreamDescriptor(kind: .screenAudio, deviceId: nil, label: "Desktop audio"))
             if result == .ok {
                 screenStreamId = streamId
-                shareScreenButton?.title = "Stop Screen Audio"
-                shareScreenButton?.image = NSImage(systemSymbolName: "rectangle.on.rectangle.angled.fill",
-                                                   accessibilityDescription: "Stop Screen Audio")
-                addActivity("Started sharing screen audio")
+                setShareScreenButton(active: true)
+                addActivity("Starting screen audio share…")
             } else {
                 addActivity("Failed to start screen audio: \(result)")
             }
         } else {
+            stopScreenCapture()
             client.stopStream(screenStreamId)
             screenStreamId = 0
-            shareScreenButton?.title = "Share Screen Audio"
-            shareScreenButton?.image = NSImage(systemSymbolName: "rectangle.on.rectangle.angled",
-                                               accessibilityDescription: "Share Screen Audio")
+            setShareScreenButton(active: false)
             addActivity("Stopped sharing screen audio")
         }
     }
 
+    private func setShareScreenButton(active: Bool) {
+        shareScreenButton?.title = active ? "Stop Screen Audio" : "Share Screen Audio"
+        shareScreenButton?.image = NSImage(
+            systemSymbolName: active ? "rectangle.on.rectangle.angled.fill" : "rectangle.on.rectangle.angled",
+            accessibilityDescription: active ? "Stop Screen Audio" : "Share Screen Audio")
+    }
+
+    /// Start ScreenCaptureKit capture for our own SCREEN_AUDIO stream. Called from the
+    /// `.streamStarted` event handler, where the effective audio config is available. Captures
+    /// in the channel's mode (stereo when the channel is stereo) and feeds 20 ms PCM frames.
+    private func startScreenCapture() {
+        guard screenStreamId != 0, screenCapture == nil else { return }
+        let (cfgResult, cfg) = client.getStreamAudioConfig(userId: selfUserId, streamId: screenStreamId)
+        let channels: UInt32 = (cfgResult == .ok && cfg?.stereo == true) ? 2 : 1
+
+        let streamId = screenStreamId
+        let capture = ScreenAudioCapture(channels: channels) { [weak self] pcm, samples, ch in
+            self?.client.feedPcm(streamId: streamId, pcm: pcm, samplesPerChannel: samples, channels: ch)
+        }
+        screenCapture = capture
+
+        Task { @MainActor in
+            do {
+                try await capture.start()
+                addActivity("Started sharing screen audio (\(channels == 2 ? "stereo" : "mono"))")
+            } catch {
+                // Most commonly: Screen Recording permission denied. Roll back the stream.
+                screenCapture = nil
+                if screenStreamId != 0 {
+                    client.stopStream(screenStreamId)
+                    screenStreamId = 0
+                    setShareScreenButton(active: false)
+                }
+                addActivity("Screen audio capture failed — grant Screen Recording in System "
+                            + "Settings ▸ Privacy & Security, then try again. (\(error))")
+            }
+        }
+    }
+
+    private func stopScreenCapture() {
+        screenCapture?.stop()
+        screenCapture = nil
+    }
+
     @objc private func muteChanged() {
         let muted = muteButton?.state == .on
         let deafened = deafenButton?.state == .on
@@ -999,6 +1049,7 @@ final class MainWindowController: NSWindowController, NSWindowDelegate {
             }
         }
         client.setPushToTalk(false)
+        stopScreenCapture()
         if screenStreamId != 0 { client.stopStream(screenStreamId) }
         if micStreamId != 0 { client.stopStream(micStreamId) }
         client.onLevel = nil