[iOS] The caret goes under the keyboard in multiline TextInput after the ScrollView auto-scrolls to the caret

Description

On iOS, when using a multiline TextInput inside a ScrollView with automaticallyAdjustKeyboardInsets, the caret goes under the keyboard after adding a new line in the input.

Steps to reproduce

<ScrollView automaticallyAdjustKeyboardInsets>
   // Any content above the TextInput to position it at the bottom of the screen
   <TextInput multiline style={{ height: 100 }} /> // multiline TextInput with some fixed height
</ScrollView>

1. ScrollView with automaticallyAdjustKeyboardInsets (with enough content to fill the whole screen).
2. Multiline TextInput with fixed height (let's say 100).
3. Focus on the input when it’s positioned at the bottom of the screen.
4. Let the keyboard slide up and the ScrollView scroll to the caret.
5. Type more than 1 line in the TextInput.
6. The TextInput caret goes under the keyboard
7. Once the TextInput fills the available height, it starts scrolling, but the user only sees the first line of the input

React Native Version

0.79.5

Affected Platforms

Runtime - iOS

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

This is not relevant

Stacktrace or Logs

This is not relevant

MANDATORY Reproducer

https://snack.expo.dev/@serge0n/textinput-multiline-autoscroll-on-new-line?platform=ios

Screenshots and Videos

https://github.com/user-attachments/assets/954d5545-3d89-4ef2-91d8-15214b4fffbe

Start by running the linked Snack reproducer on iOS and trace the interaction between ScrollView's automaticallyAdjustKeyboardInsets and the multiline TextInput. Compare caret visibility before and after entering a new line; done means the caret remains above the keyboard and the visible text follows the caret as the input fills.