TextInput value cannot be manipulated via setNativeProps after user input on iOS

Description

When an uncontrolled TextInput has had its value manipulated via setNativeProps, receives user input and is then manipulated again via setNativeProps, the displayed value does not change.

This looks to be a New Arch issue and the issue is not reproducible in 0.76.0 on the old architecture.

Steps to reproduce

1. Install the application with yarn ios
2. Press "Press me!"
3. Note that the TextInput contains the text "bananas"
4. Clear the input field
5. Press "Press me!"
6. Note that the input field remains empty

React Native Version

0.76.0

Affected Platforms

Runtime - iOS

Areas

Fabric - The New Renderer

Output of npx react-native info

System:
  OS: macOS 14.7
  CPU: (16) arm64 Apple M3 Max
  Memory: 2.53 GB / 48.00 GB
  Shell:
    version: "5.9"
    path: /bin/zsh
Binaries:
  Node:
    version: 18.20.4
    path: /opt/homebrew/Cellar/node@18/18.20.4_1/bin/node
  Yarn:
    version: 1.22.22
    path: /opt/homebrew/bin/yarn
  npm:
    version: 10.7.0
    path: /opt/homebrew/Cellar/node@18/18.20.4_1/bin/npm
  Watchman: Not Found
Managers:
  CocoaPods:
    version: 1.15.2
    path: /opt/homebrew/bin/pod
SDKs:
  iOS SDK:
    Platforms:
      - DriverKit 24.0
      - iOS 18.0
      - macOS 15.0
      - tvOS 18.0
      - visionOS 2.0
      - watchOS 11.0
  Android SDK: Not Found
IDEs:
  Android Studio: Not Found
  Xcode:
    version: 16.0/16A242d
    path: /usr/bin/xcodebuild
Languages:
  Java: Not Found
  Ruby:
    version: 2.6.10
    path: /usr/bin/ruby
npmPackages:
  "@react-native-community/cli":
    installed: 15.0.0-alpha.2
    wanted: 15.0.0-alpha.2
  react:
    installed: 18.3.1
    wanted: 18.3.1
  react-native:
    installed: 0.76.0
    wanted: 0.76.0
  react-native-macos: Not Found
npmGlobalPackages:
  "*react-native*": Not Found
Android:
  hermesEnabled: true
  newArchEnabled: true
iOS:
  hermesEnabled: true
  newArchEnabled: true

Stacktrace or Logs

None

Reproducer

https://github.com/mhoran/new-arch-set-text-repro/

Screenshots and Videos

No response

Use the linked new-arch-set-text-repro repository and run it with yarn ios under the reported React Native 0.76.0 New Architecture configuration. Reproduce the sequence of setting “bananas,” entering user input, clearing it, and pressing the button again; done means the second native update changes the displayed TextInput value.