The problem is, after expanding the bottom sheet, the area underneath the sheet where the MaterialToolbar is located can't be used to drag the sheet back down. The rest of the sheet can still be used for dragging.
Complete runnable project is at https://github.com/svenoaks/DragBottomSheet
I used the standard Material3 Android Studio project and modified it like this:
activity_main.xml
<?xml version="1.0" encoding="utf-8"?>
<androidx.coordinatorlayout.widget.CoordinatorLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:fitsSystemWindows="true"
tools:context=".MainActivity">
<com.google.android.material.appbar.AppBarLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:fitsSystemWindows="true">
<com.google.android.material.appbar.MaterialToolbar
android:id="@+id/toolbar"
android:layout_width="match_parent"
app:layout_collapseMode="none"
android:layout_height="128dp" />
</com.google.android.material.appbar.AppBarLayout>
<FrameLayout
android:id="@+id/standard_bottom_sheet"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:background="?colorSecondary"
app:layout_behavior="com.google.android.material.bottomsheet.BottomSheetBehavior"
app:behavior_hideable="false"
app:behavior_peekHeight="?actionBarSize">
<include layout="@layout/content_main" />
</FrameLayout>
</androidx.coordinatorlayout.widget.CoordinatorLayout>