After xxx, a purple cursor appears and I want to know the name of the falling cursor so I can change its color to match my theme. I have read many forums and documentation, but all I found was cursorDrawable, which is not what I am looking for. Please help me find the correct name or solution. Thank you. PD: The purple color of the cursor is not in the style or color I am using.

Solutip
The key is in colorPrimary
and you just override it to the color you want, for example:
<com.google.android.material.textfield.TextInputLayout
style="@style/Widget.MaterialComponents.TextInputLayout.OutlinedBox"
android:theme="@style/ThemeOverlay.AppTheme.TextInputEditText.Outlined"
....>
with
<style name="ThemeOverlay.AppTheme.TextInputEditText.Outlined" parent="">
<item name="colorPrimary">@color/...</item>
</style>
become
or just want to override the cursor
<style name="ThemeOverlay.AppTheme.TextInputEditText.Outlined" parent="">
<item name="colorControlActivated">@color/...</item>
</style>
so it becomes like this
done.