Outgoing iOS screen-share via ReplayKit broadcast extension

Lets a native-call user share their iPhone screen (whole device, works
backgrounded). LiveKit 2.15.3 ships the broadcast stack (BroadcastManager +
LKSampleHandler + IPC), so:

- New Broadcast Upload Extension target "BroadcastExtension"
  (com.bizgaze.connect.broadcast): SampleHandler.swift subclasses
  LKSampleHandler; injected by mobile/scripts/add-broadcast-extension.rb
  which also LINKS the LiveKit SPM product into the extension + sets the
  App Group. Sources in mobile/ios-broadcast/.
- Plugin: Room created with ScreenShareCaptureOptions(useBroadcastExtension:
  true); startScreenShare -> BroadcastManager.requestActivation() (system
  picker); stopScreenShare -> requestStop(); BroadcastManagerDelegate ->
  fires screenShareState to the web. LiveKit auto-publishes the track.
- ios-patch.sh: RTCScreenSharingExtension + RTCAppGroupIdentifier keys.
- codemagic.yaml: run the injector + sign the 3rd bundle id (.broadcast).
- home.html: toggleScreen native -> start/stop; screenShareState listener
  reflects state + broadcasts meeting-screen so peers' stage shows it.

REQUIRES a one-time manual Apple portal step: enable the App Group on the
com.bizgaze.connect.broadcast App ID (see mobile/IOS_SETUP.md) or the
archive fails code-signing. SPM-linked extension is new on our CI — expect
build iteration. Web deployed (no-ops on builds without startScreenShare).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

mobile/ios-broadcast/BroadcastExtension.entitlements

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+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>com.apple.security.application-groups</key>
+	<array>
+		<string>group.com.bizgaze.connect</string>
+	</array>
+</dict>
+</plist>

mobile/ios-broadcast/Info.plist

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+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDisplayName</key>
+	<string>Biz Connect Screen</string>
+	<key>CFBundleName</key>
+	<string>$(PRODUCT_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundlePackageType</key>
+	<string>$(PRODUCT_BUNDLE_PACKAGE_TYPE)</string>
+	<key>CFBundleShortVersionString</key>
+	<string>$(MARKETING_VERSION)</string>
+	<key>CFBundleVersion</key>
+	<string>$(CURRENT_PROJECT_VERSION)</string>
+	<key>NSExtension</key>
+	<dict>
+		<key>NSExtensionPointIdentifier</key>
+		<string>com.apple.broadcast-services-upload</string>
+		<key>NSExtensionPrincipalClass</key>
+		<string>$(PRODUCT_MODULE_NAME).SampleHandler</string>
+		<key>RPBroadcastProcessMode</key>
+		<string>RPBroadcastProcessModeSampleBuffer</string>
+	</dict>
+</dict>
+</plist>

mobile/ios-broadcast/SampleHandler.swift

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+import ReplayKit
+import LiveKit
+
+// Principal class of the Broadcast Upload Extension (ReplayKit) that lets the iOS user share their screen.
+//
+// HOW IT WORKS: when the user starts a system broadcast, iOS launches THIS extension. LiveKit's LKSampleHandler
+// does everything — on broadcastStarted it opens an IPC socket in the shared App Group (group.com.bizgaze.connect)
+// and streams the ReplayKit sample buffers to the MAIN app, whose LiveKit connection publishes them as a
+// screen-share track. The extension itself never creates a Room / initialises WebRTC, so it stays well under the
+// 50 MB extension memory limit. So this subclass can be empty.
+//
+// The extension finds the app group + reports state to the app via LiveKit's Darwin-notification/socket
+// convention, keyed off this extension's bundle id (com.bizgaze.connect.broadcast) and the default app group
+// group.<appBundleId>. Both are also set explicitly on the app side (RTCScreenSharingExtension /
+// RTCAppGroupIdentifier in Info.plist) so there's no ambiguity.
+class SampleHandler: LKSampleHandler {}