Bottom inset animation is janky and out of sync when opening the keyboard.
cc: @cyanglaz - flutter/engine#39172 (comment)

Tested on latest stable and master 3.8.0-5.0.pre.1, iphone 13 pro, ios 16.1.1

Steps to Reproduce

Please run this example here:
https://github.com/delfme/flutter-native-text-input-repo

You can disable/enable flutter textfield and native textfield by commenting/uncommenting related lines. Issue occurs with both textfields.

Expected results:
When opening keyboard, UI should animate smoothly and stay ahead of the keyboard for the most part of the run.

Actual results:
Animation is janky and the first stop is already at the 80% of entire run.

Debugging:
Things have changed during these months and latest merges, please read comments below.

Flutter doctor:

[✓] Flutter (Channel master, 3.8.0-5.0.pre.1, on macOS 12.2 21D49 darwin-arm64, locale en-IT)
[!] Android toolchain - develop for Android devices (Android SDK version 31.0.0)
✗ cmdline-tools component is missing
Run path/to/sdkmanager --install "cmdline-tools;latest"
See https://developer.android.com/studio/command-line for more details.
✗ Android license status unknown.
Run flutter doctor --android-licenses to accept the SDK licenses.
See https://flutter.dev/docs/get-started/install/macos#android-setup for more details.
[✓] Xcode - develop for iOS and macOS (Xcode 13.4.1)
[✓] Chrome - develop for the web
[✓] Android Studio (version 2021.2)
[✓] Connected device (3 available)
[✓] HTTP Host Availability