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

@@ -0,0 +1,10 @@
+<?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>