bug: back handler stops working after re-foregrounding the app

Description

back handlers seem to stop working after sending the app to the background - all back gestures (except in Modals) just close the app instead. see the video below for a clearer demonstration.

I'm using the Android 16 QPR2 beta (BP41.250916.015.A1) on a Pixel 8.

I can reproduce this using either the @react-native-community/hooks hook or the usage example in the BackHandler docs. the hook works fine in React Native v0.80 (I assume because the target SDK was still 35?).

Steps to reproduce

1. Start the app
2. Press the button at the top
3. Do a back gesture and observe that it respects the back handler
4. Do another one to go home
5. Re-open the app
6. Press the button at the top again
7. Do another back gesture and observe that it exits out of the app instead of respecting the back handler

React Native Version

0.83.0

Affected Platforms

Runtime - Android, Build - Linux

Output of npx @react-native-community/cli info

System:
  OS: Linux 6.17 Ubuntu 25.10 25.10 (Questing Quokka)
  CPU: (8) x64 Intel(R) Core(TM) Ultra 7 256V
  Memory: 4.46 GB / 14.72 GB
  Shell:
    version: 5.2.37
    path: /bin/bash
Binaries:
  Node:
    version: 24.5.0
    path: /home/rexo/.nvm/versions/node/v24.5.0/bin/node
  Yarn:
    version: 4.12.0
    path: /home/rexo/.nvm/versions/node/v24.5.0/bin/yarn
  npm:
    version: 11.5.1
    path: /home/rexo/.nvm/versions/node/v24.5.0/bin/npm
  Watchman: Not Found
SDKs:
  Android SDK:
    API Levels:
      - "31"
      - "35"
      - "36"
    Build Tools:
      - 34.0.0
      - 35.0.0
      - 35.0.1
      - 36.0.0
    System Images:
      - android-35 | Google APIs Intel x86_64 Atom
      - android-35 | Google Play Intel x86_64 Atom
      - android-36 | Google Play Intel x86_64 Atom
    Android NDK: Not Found
IDEs:
  Android Studio: Not Found
Languages:
  Java:
    version: 17.0.17
    path: /usr/bin/javac
  Ruby: Not Found
npmPackages:
  "@react-native-community/cli":
    installed: 20.0.0
    wanted: 20.0.0
  react:
    installed: 19.2.0
    wanted: 19.2.0
  react-native:
    installed: 0.83.0
    wanted: 0.83.0
npmGlobalPackages:
  "*react-native*": Not Found
Android:
  hermesEnabled: true
  newArchEnabled: true
iOS:
  hermesEnabled: Not found
  newArchEnabled: false

Stacktrace or Logs

N/A

MANDATORY Reproducer

https://github.com/Rexogamer/backhandler-test

Screenshots and Videos

https://github.com/user-attachments/assets/a48256a0-d956-446d-b5da-1ceccc824d91

Start with the mandatory reproducer and the BackHandler usage example linked in the issue, running it on Android 16 QPR2 with React Native 0.83. Compare back-handler behavior before backgrounding and after re-opening the app. Done means registered handlers continue to run after the app returns to the foreground instead of the back gesture exiting the app.