Refresh haptics is broken after RefreshControl remount

Description

Refresh haptics is broken after RefreshControl remount.
Disabling view recycling for RCTPullToRefreshViewComponentView fixes the issue.

Steps to reproduce

1. Run the repro project on a physical device
2. Refresh - haptics works
3. Click remount
4. Refresh again - haptics gone

React Native Version

0.86.2

Affected Platforms

Runtime - iOS

Areas

Fabric - The New Renderer

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

System:
  OS: macOS 26.5.2
  CPU: (11) arm64 Apple M3 Pro
  Memory: 140.80 MB / 18.00 GB
  Shell:
    version: "5.9"
    path: /bin/zsh
Binaries:
  Node:
    version: 24.18.0
    path: /Users/oleksiibulenok/.nvm/versions/node/v24.18.0/bin/node
  Yarn:
    version: 1.22.22
    path: /Users/oleksiibulenok/.nvm/versions/node/v24.18.0/bin/yarn
  npm:
    version: 11.16.0
    path: /Users/oleksiibulenok/.nvm/versions/node/v24.18.0/bin/npm
  Watchman: Not Found
Managers:
  CocoaPods:
    version: 1.16.2
    path: /opt/homebrew/bin/pod
SDKs:
  iOS SDK:
    Platforms:
      - DriverKit 25.5
      - iOS 26.5
      - macOS 26.5
      - tvOS 26.5
      - visionOS 26.5
      - watchOS 26.5
  Android SDK:
    API Levels:
      - "34"
      - "35"
      - "36"
    Build Tools:
      - 34.0.0
      - 35.0.0
      - 36.0.0
    System Images:
      - android-35 | Google Play ARM 64 v8a
      - android-36 | Google Play ARM 64 v8a
    Android NDK: Not Found
IDEs:
  Android Studio: 2025.1 AI-251.26094.121.2512.13991807
  Xcode:
    version: 26.6/17F113
    path: /usr/bin/xcodebuild
Languages:
  Java:
    version: 17.0.14
    path: /Users/oleksiibulenok/Library/Java/JavaVirtualMachines/jbr-17.0.14/Contents/Home/bin/javac
  Ruby:
    version: 2.7.6
    path: /Users/oleksiibulenok/.rbenv/shims/ruby
npmPackages:
  "@react-native-community/cli":
    installed: 20.1.0
    wanted: 20.1.0
  react:
    installed: 19.2.3
    wanted: 19.2.3
  react-native:
    installed: 0.86.2
    wanted: 0.86.2
  react-native-macos: Not Found
npmGlobalPackages:
  "*react-native*": Not Found
Android:
  hermesEnabled: true
  newArchEnabled: true
iOS:
  hermesEnabled: true
  newArchEnabled: true

Stacktrace or Logs

N/A

MANDATORY Reproducer

https://github.com/abulenok/rn-refresh-control-haptic-remount-repro

Screenshots and Videos

No response

Run the mandatory reproducer on a physical iOS device and confirm that haptics stop after RefreshControl remount. Then inspect RCTPullToRefreshViewComponentView and its view recycling behavior in the Fabric implementation. Done means refresh haptics work both before and after the component is remounted.