Repository: react-native
Issue: Animated Value listeners removed after bound elements unmounted
Labels: Issue: Author Provided Repro,API: Animated

### Description

If an animated value is attached to an animated view as a transform, and the view is unmounted, all listeners on the animated value are removed and cease to fire. The animation continues to be active, and new listeners can be added, but the original listeners are all removed. This does not happen in react-native-web, and expo snack cannot replicate the problem.

### Steps to reproduce

- Open the sample application
- Notice that the state value at the top (text) and the green box (Animated.View) are both changing
- Hit the `Remount animation` button to unmount, and re-mount the animation (changing `key`)
- See that the state value has stopped changing

The animated value listener attached to the animated value has stopped listening now, and won't fire any more.

### Findings

In `Libraries/Animated/useAnimatedProps.js#167`: 

```ts
  useLayoutEffect(() => {
    node.__attach();
    if (prevNodeRef.current != null) {
      const prevNode = prevNodeRef.current;
      // TODO: Stop restoring default values (unless `reset` is called).
      prevNode.__restoreDefaultValues();
      prevNode.__detach();
      prevNodeRef.current = null;
    }
    return () => {
      if (isUnmountingRef.current) {
        // NOTE: Do not restore default values on unmount, see D18197735.
        node.__detach();   <-------- here
      } else {
        prevNodeRef.current = node;
      }
    };
  }, [node]);
```

This line seems to be detaching the animated props node, which calls `removeAllListeners` on the AnimatedNode and kills the listener. However, an animated value can have a lifespan longer than any component that uses it and may have other listeners that are doing important things, so I think this is a bug – especially because it doesn't happen in react-native-web.

I suspect the fix may involve tracking which listeners are added specifically by the node and removing those specifically (instead of calling `removeAllListeners`). I don't know what level of effort is involved here but I would be more than happy to help test or prototype a fix for this.

### React Native Version

0.73.6

### Affected Platforms

Runtime - Android, Runtime - iOS

### Output of `npx react-native info`

```text
info Fetching system and libraries information...
System:
  OS: macOS 14.3.1
  CPU: (10) arm64 Apple M1 Max
  Memory: 142.38 MB / 64.00 GB
  Shell:
    version: "5.9"
    path: /bin/zsh
Binaries:
  Node:
    version: 20.8.1
    path: ~/.nvm/versions/node/v20.8.1/bin/node
  Yarn:
    version: 1.22.21
    path: /opt/homebrew/bin/yarn
  npm:
    version: 10.1.0
    path: ~/.nvm/versions/node/v20.8.1/bin/npm
  Watchman:
    version: 2024.01.22.00
    path: /opt/homebrew/bin/watchman
Managers:
  CocoaPods:
    version: 1.15.2
    path: /Users/elliott/.rbenv/shims/pod
SDKs:
  iOS SDK:
    Platforms:
      - DriverKit 23.4
      - iOS 17.4
      - macOS 14.4
      - tvOS 17.4
      - visionOS 1.1
      - watchOS 10.4
  Android SDK:
    API Levels:
      - "28"
      - "33"
      - "34"
    Build Tools:
      - 28.0.3
      - 29.0.2
      - 29.0.3
      - 30.0.2
      - 30.0.3
      - 31.0.0
      - 33.0.0
      - 34.0.0
    System Images:
      - android-33 | Google APIs ARM 64 v8a
      - android-34 | ARM 64 v8a
      - android-34 | Google APIs ARM 64 v8a
      - android-34 | Google Play ARM 64 v8a
    Android NDK: Not Found
IDEs:
  Android Studio: 2022.3 AI-223.8836.35.2231.10406996
  Xcode:
    version: 15.3/15E204a
    path: /usr/bin/xcodebuild
Languages:
  Java:
    version: 17.0.10
    path: /usr/bin/javac
  Ruby:
    version: 3.0.0
    path: /Users/elliott/.rbenv/shims/ruby
npmPackages:
  "@react-native-community/cli": Not Found
  react:
    installed: 18.2.0
    wanted: 18.2.0
  react-native:
    installed: 0.73.6
    wanted: 0.73.6
  react-native-macos: Not Found
npmGlobalPackages:
  "*react-native*": Not Found
Android:
  hermesEnabled: true
  newArchEnabled: false
iOS:
  hermesEnabled: true
  newArchEnabled: false
```

### Reproducer

https://github.com/elliottkember/animation-listener-bug

### Screenshots and Videos

In this video, the `Remount animation` button simply changes the key on the Animated.View element that keeps changing size.

https://github.com/facebook/react-native/assets/42827/eab17e92-edd1-404a-963a-0a003d14c1ef