Timers don't work in headless tasks and may break in the application when headless tasks are used

[j-piasecki]

Description

JavaTimerManager is being registered to receive headless tasks events in the TimingModule, which isn't used on Bridgeless. Due to this, timers don't work in headless tasks unless the app is in the foreground, and minimizing/reopening the app may entirely break the timers.

Steps to reproduce

1. Build the android app
2. Click on the SetTimeout button
3. Observe console log after 2 seconds
4. Click StartService (the app will close)
5. There are no logs from the service unless the app is in foreground (timeouts don't work in the headless task)
6. Reopen the app
7. Go back to home screen
8. Go back to the app
9. Click on the SetTimeout button
10. Timeouts don't work in the app at all

React Native Version

0.76.1

Affected Platforms

Runtime - Android

Areas

Bridgeless - The New Initialization Flow

Output of npx react-native info

System:
  OS: macOS 14.7
  CPU: (12) arm64 Apple M3 Pro
  Memory: 106.73 MB / 18.00 GB
  Shell:
    version: "5.9"
    path: /bin/zsh
Binaries:
  Node:
    version: 20.18.0
    path: ~/.nvm/versions/node/v20.18.0/bin/node
  Yarn:
    version: 3.6.4
    path: /opt/homebrew/bin/yarn
  npm:
    version: 10.8.2
    path: ~/.nvm/versions/node/v20.18.0/bin/npm
  Watchman:
    version: 2024.09.09.00
    path: /opt/homebrew/bin/watchman
Managers:
  CocoaPods: Not Found
SDKs:
  iOS SDK:
    Platforms:
      - DriverKit 23.5
      - iOS 17.5
      - macOS 14.5
      - tvOS 17.5
      - visionOS 1.2
      - watchOS 10.5
  Android SDK:
    API Levels:
      - "24"
      - "26"
      - "28"
      - "29"
      - "30"
      - "31"
      - "32"
      - "33"
      - "34"
      - "35"
    Build Tools:
      - 26.0.3
      - 28.0.3
      - 29.0.2
      - 29.0.3
      - 30.0.2
      - 30.0.3
      - 31.0.0
      - 32.0.0
      - 32.1.0
      - 33.0.0
      - 33.0.1
      - 34.0.0
      - 35.0.0
      - 35.0.0
    System Images:
      - android-28 | Google ARM64-V8a Play ARM 64 v8a
      - android-33 | Google APIs ARM 64 v8a
      - android-34 | Google Play ARM 64 v8a
      - android-35 | Google Play ARM 64 v8a
    Android NDK: Not Found
IDEs:
  Android Studio: 2024.2 AI-242.23339.11.2421.12483815
  Xcode:
    version: 15.4/15F31d
    path: /usr/bin/xcodebuild
Languages:
  Java:
    version: 17.0.2
    path: /usr/bin/javac
  Ruby:
    version: 2.7.5
    path: /Users/jakubpiasecki/.rvm/rubies/ruby-2.7.5/bin/ruby
npmPackages:
  "@react-native-community/cli":
    installed: 15.0.0
    wanted: 15.0.0
  react:
    installed: 18.3.1
    wanted: 18.3.1
  react-native:
    installed: 0.76.1
    wanted: 0.76.1
  react-native-macos: Not Found
npmGlobalPackages:
  "*react-native*": Not Found
Android:
  hermesEnabled: true
  newArchEnabled: true
iOS:
  hermesEnabled: Not found
  newArchEnabled: false

### Stacktrace or Logs

```text
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Reproducer

https://github.com/j-piasecki/timer-headless-task-issue

Screenshots and Videos

Screen.Recording.2024-11-07.at.16.51.40.mov