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/iOS/VoiceCatiOS/Views/VoiceControlsView.swift

@@ -1,5 +1,6 @@
 import SwiftUI
 import VoiceCatCore
+import ReplayKit
 
 struct VoiceControlsView: View {
     @Bindable var session: SessionState
@@ -58,6 +59,14 @@ struct VoiceControlsView: View {
             .disabled(!session.voiceState.micActive)
             .accessibilityLabel(session.voiceState.selfDeafened ? "Undeafen" : "Deafen")
 
+            // Share screen audio (ReplayKit system broadcast picker). The picker launches the
+            // broadcast upload extension; the host's BroadcastAudioPump then owns + feeds the
+            // SCREEN_AUDIO stream. Tinted while sharing.
+            BroadcastPickerButton(isSharing: session.voiceState.screenSharing)
+                .frame(width: 32, height: 32)
+                .accessibilityLabel(session.voiceState.screenSharing
+                                    ? "Stop sharing screen audio" : "Share screen audio")
+
             // Disconnect
             Button(role: .destructive) {
                 session.stopMicStream()
@@ -108,6 +117,26 @@ private struct PTTButton: View {
     }
 }
 
+// MARK: - Broadcast picker
+
+/// Wraps `RPSystemBroadcastPickerView` (which contains its own button) and points it at our
+/// broadcast upload extension. Tapping it shows the system broadcast picker; the user starts the
+/// broadcast and our extension launches.
+private struct BroadcastPickerButton: UIViewRepresentable {
+    let isSharing: Bool
+
+    func makeUIView(context: Context) -> RPSystemBroadcastPickerView {
+        let picker = RPSystemBroadcastPickerView(frame: CGRect(x: 0, y: 0, width: 32, height: 32))
+        picker.preferredExtension = "cat.voice.VoiceCatiOS.broadcast"
+        picker.showsMicrophoneButton = false
+        return picker
+    }
+
+    func updateUIView(_ uiView: RPSystemBroadcastPickerView, context: Context) {
+        uiView.tintColor = isSharing ? .systemGreen : .label
+    }
+}
+
 // MARK: - Level Meter
 
 private struct LevelMeterView: View {