Refresh haptics is broken after RefreshControl remount

[abulenok]

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