[bug] iOS: `useiOSBroadcastExtension: false` ignored since 2.4.0, in-app capture unreachable

[VladGrant]

Describe the bug

Since 2.4.0, setScreenShareEnabled(true) on iOS unconditionally routes into the Broadcast Upload Extension flow. ScreenShareCaptureOptions.useiOSBroadcastExtension still exists, but false (the documented in-app RPScreenRecorder mode through 2.3.6) has no effect.

lib/src/participant/local.dart (2.4.0–2.10.0 and current main):

if (lkPlatformIs(PlatformType.iOS) && !BroadcastManager().isBroadcasting) {
  // Wait until broadcasting to publish track
  await BroadcastManager().requestActivation();
  return null;
}

The branch precedes any capture options inspection; the in-app path below it is unreachable.

Worse, without an extension: requestActivation()'s native side (ios/Classes/BroadcastManager.swift) guard-returns when the RTCScreenSharingExtension Info.plist key is absent:

func requestActivation() {
    guard let bundleIdentifier = BroadcastBundleInfo.screenSharingExtension else { return }
    Task { await Self.showPicker(for: bundleIdentifier) }
}

No picker, no consent UI, no error, and no log so the call resolves null as success.

This appears to be an unintended side effect of #705 ("fix: Properly handle broadcast capture state"): the PR documents its async-return breaking change but never mentions useiOSBroadcastExtension or the in-app path. That capturer still works in flutter_webrtc, reachable via LocalVideoTrack.createScreenShareTrack() + publishVideoTrack() which is our current workaround.

Broadcast extension capture is always whole screen; in-app capture is scoped to the app's own UI. For privacy sensitive products (share this app with a support agent, never the user's other apps or notifications), app scoped capture is impossible through the public screenshare API on every released version.

To Reproduce

1. Flutter app on a physical iPhone, livekit_client ≥ 2.4.0, no Broadcast Upload Extension target.
2. Connect to a room, then:

   await room.localParticipant!.setScreenShareEnabled(
     true,
     screenShareCaptureOptions:
         const ScreenShareCaptureOptions(useiOSBroadcastExtension: false),
   );

3. The call resolves (null); no consent UI, no published track, nothing logged. Remote participants receive nothing.
4. On 2.3.6 the same code shows the ReplayKit consent alert and publishes an in-app screenshare track.

Expected behavior

• useiOSBroadcastExtension: false (explicit or via RoomOptions.defaultScreenShareCaptureOptions) uses the in-app capturer, as through 2.3.6 . The gate should consult the effective capture options before routing to BroadcastManager.
• Independently: when the broadcast flow is requested but RTCScreenSharingExtension is missing, fail loudly (throw or error event) instead of a silent null. Currently misconfiguration looks like success.

Platform information

• Flutter version: 3.44.2
• Plugin version: reproduced on 2.7.0 and 2.10.0 ; unchanged on main, 2026-08-04
• Flutter target OS: iOS (real device, iPhone 17)
• Flutter target OS version: iOS 26.4
• Flutter console log: n/a, failure produces no output