[ModalBottomSheet] The screen reader reaches the screen behind an open sheet

Summary

With a ModalBottomSheet open, the screen reader still reaches the elements behind it,
either by swiping forward past the last element in the sheet or by touching the backdrop.

Videos with sound:

VoiceOver on iOS

TalkBack on Android

Reproduction

https://github.com/kilarsky/swm-bottom-sheet-screen-reader-reaches-behind-repro

1. Turn VoiceOver or TalkBack on.
2. Tap Open sheet.
3. Put reader focus on the Sheet heading, then swipe forward past Close.
4. Or touch the backdrop above the sheet.

Expected

Focus stays in the sheet.

Actual

The reader reaches the background either way, even though the backdrop covers it.

Environment

@swmansion/react-native-bottom-sheet: 0.16.2

iOS 26.5 and Android 11 in the videos.

  expo-env-info 2.1.0 environment info:
    System:
      OS: macOS 26.5.2
      Shell: 5.9 - /bin/zsh
    Binaries:
      Node: 22.18.0 - /usr/local/bin/node
      Yarn: 1.22.22 - /usr/local/bin/yarn
      npm: 10.9.3 - /usr/local/bin/npm
      Watchman: 2025.09.15.00 - /opt/homebrew/bin/watchman
    Managers:
      CocoaPods: 1.16.2 - /Users/.../.rbenv/shims/pod
    SDKs:
      iOS SDK:
        Platforms: DriverKit 25.5, iOS 26.5, macOS 26.5, tvOS 26.5, visionOS 26.5, watchOS 26.5
    IDEs:
      Android Studio: 2026.1 AI-261.26222.65.2613.16025427
      Xcode: 26.5/17F42 - /usr/bin/xcodebuild
    npmPackages:
      expo: ~57.0.15 => 57.0.15 
      react: 19.2.3 => 19.2.3 
      react-native: 0.86.2 => 0.86.2 
    Expo Workflow: bare

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Start with the linked reproduction app and follow the VoiceOver and TalkBack steps with a ModalBottomSheet open. Verify the behavior on both platforms, then confirm the fix when reader focus remains within the sheet after swiping past Close or touching the backdrop.