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