Basic example of a custom draggable drawer in Android.

activity_main_drawer_closed.xml

<!-- File : app/src/main/res/layout/activity_main_drawer_closed.xml -->

<?xml version="1.0" encoding="utf-8"?>
<androidx.constraintlayout.widget.ConstraintLayout
    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:clipChildren="false"
    android:id="@+id/rootConstraintLayout"
    tools:context=".MainActivity">

    <androidx.constraintlayout.widget.ConstraintLayout
        android:id="@+id/drawerConstraintLayout"
        android:layout_width="152dp"
        android:layout_height="108dp"
        android:background="@color/colorPrimaryDark"
        app:layout_constraintTop_toTopOf="parent"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintStart_toEndOf="parent" >

        <Button
            android:id="@+id/button1"
            android:layout_width="52dp"
            android:layout_height="52dp"
            android:text="1"
            android:backgroundTint="@color/colorAccent"
            app:layout_constraintTop_toTopOf="parent"
            app:layout_constraintBottom_toBottomOf="parent"
            app:layout_constraintStart_toStartOf="parent"
            app:layout_constraintEnd_toStartOf="@id/button2" />

        <Button
            android:id="@+id/button2"
            android:layout_width="52dp"
            android:layout_height="52dp"
            android:text="2"
            android:backgroundTint="@color/colorAccent"
            app:layout_constraintTop_toTopOf="parent"
            app:layout_constraintBottom_toBottomOf="parent"
            app:layout_constraintStart_toEndOf="@id/button1"
            app:layout_constraintEnd_toEndOf="parent" />

    </androidx.constraintlayout.widget.ConstraintLayout>

    <ImageView
        android:id="@+id/notch"
        android:layout_width="8dp"
        android:layout_height="72dp"
        android:src="@drawable/drawer_notch"
        app:layout_constraintTop_toTopOf="parent"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintEnd_toStartOf="@id/drawerConstraintLayout" />

</androidx.constraintlayout.widget.ConstraintLayout>

activity_main_drawer_opened.xml

<!-- File : app/src/main/res/layout/activity_main_drawer_opened.xml -->

<?xml version="1.0" encoding="utf-8"?>
<androidx.constraintlayout.widget.ConstraintLayout
    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:id="@+id/rootConstraintLayout"
    tools:context=".MainActivity">

    <androidx.constraintlayout.widget.ConstraintLayout
        android:id="@+id/drawerConstraintLayout"
        android:layout_width="152dp"
        android:layout_height="108dp"
        android:background="@color/colorPrimaryDark"
        app:layout_constraintTop_toTopOf="parent"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintEnd_toEndOf="parent" >

        <Button
            android:id="@+id/button1"
            android:layout_width="52dp"
            android:layout_height="52dp"
            android:text="1"
            android:backgroundTint="@color/colorAccent"
            app:layout_constraintTop_toTopOf="parent"
            app:layout_constraintBottom_toBottomOf="parent"
            app:layout_constraintStart_toStartOf="parent"
            app:layout_constraintEnd_toStartOf="@id/button2" />

        <Button
            android:id="@+id/button2"
            android:layout_width="52dp"
            android:layout_height="52dp"
            android:text="2"
            android:backgroundTint="@color/colorAccent"
            app:layout_constraintTop_toTopOf="parent"
            app:layout_constraintBottom_toBottomOf="parent"
            app:layout_constraintStart_toEndOf="@id/button1"
            app:layout_constraintEnd_toEndOf="parent" />

    </androidx.constraintlayout.widget.ConstraintLayout>

    <ImageView
        android:id="@+id/notch"
        android:layout_width="8dp"
        android:layout_height="72dp"
        android:src="@drawable/drawer_notch"
        app:layout_constraintTop_toTopOf="parent"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintEnd_toStartOf="@id/drawerConstraintLayout" />

</androidx.constraintlayout.widget.ConstraintLayout>

build.gradle

// File : app/build.gradle

apply plugin: 'com.android.application'

android {
    compileSdkVersion 29
    buildToolsVersion "29.0.2"

    defaultConfig {
        minSdkVersion 19
        targetSdkVersion 29
    }
}

dependencies {
    implementation 'androidx.appcompat:appcompat:1.1.0'
    implementation 'androidx.constraintlayout:constraintlayout:1.1.3'
}

drawer_notch.xml

<!-- File : app/src/main/res/drawable/drawer_notch.xml -->

<?xml version="1.0" encoding="utf-8"?>
<shape
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:shape="rectangle">
    <corners android:radius="4dp" />
    <solid android:color="@color/colorAccent" />
</shape>

MainActivity.java

// File : app/src/main/java/<package_path>/MainActivity.java

import androidx.appcompat.app.AppCompatActivity;
import androidx.constraintlayout.widget.ConstraintLayout;
import androidx.constraintlayout.widget.ConstraintSet;
import androidx.core.view.GestureDetectorCompat;

import android.os.Bundle;
import android.transition.TransitionManager;
import android.view.GestureDetector;
import android.view.MotionEvent;

public class MainActivity extends AppCompatActivity {

    private boolean mIsDrawerOpened;
    private ConstraintLayout mRootConstraintLayout;
    private final ConstraintSet mDrawerClosedConstraintSet = new ConstraintSet();
    private final ConstraintSet mDrawerOpenedConstraintSet = new ConstraintSet();
    private GestureDetectorCompat mGestureDetector;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main_drawer_closed);

        // Drawer is initially closed
        mIsDrawerOpened = false;

        mRootConstraintLayout = findViewById(R.id.rootConstraintLayout);

        mDrawerClosedConstraintSet.clone(this, R.layout.activity_main_drawer_closed);
        mDrawerOpenedConstraintSet.clone(this, R.layout.activity_main_drawer_opened);

        mGestureDetector = new GestureDetectorCompat(
                getApplicationContext(),
                new GestureDetector.SimpleOnGestureListener() {

                    @Override
                    public boolean onFling(MotionEvent e1, MotionEvent e2, float velocityX, float velocityY) {

                        // Drag / Fling gesture detected

                        // TODO: Recongnize unwanted drag / fling gestures and ignore them.

                        TransitionManager.beginDelayedTransition(mRootConstraintLayout);

                        // Drawer is closed?
                        if(!mIsDrawerOpened) {
                            // Open the drawer
                            mDrawerOpenedConstraintSet.applyTo(mRootConstraintLayout);
                            mIsDrawerOpened = true;
                        }

                        return true;
                    }

                    @Override
                    public boolean onSingleTapUp(MotionEvent e) {

                        // Single tap detected

                        // TODO: If user has tapped on the drawer, do not close it.

                        TransitionManager.beginDelayedTransition(mRootConstraintLayout);

                        // Drawer is opened?
                        if(mIsDrawerOpened) {
                            // Close the drawer
                            mDrawerClosedConstraintSet.applyTo(mRootConstraintLayout);
                            mIsDrawerOpened = false;
                        }

                        return true;
                    }

                    @Override
                    public boolean onDown(MotionEvent e) {
                        return true;
                    }
                }
        );
    }

    @Override
    public boolean onTouchEvent(MotionEvent event) {
        mGestureDetector.onTouchEvent(event);
        return super.onTouchEvent(event);
    }
}

I created this Github gist for a StackOverflow question as the code reference.

Answer to the StackOverflow question that fixes the issue has been included in this gist (Revision 2).