The first draft was without the linearlayout, but doing so the toolbar was overlapping the included layout.

You can go ahead with your first attempt, but just add a top margin that equals to the Toolbar height; which is the default ActionBar height in your case ?attr/actionBarSize.

So, this will be:

<com.google.android.material.appbar.AppBarLayout
    
    <com.google.android.material.appbar.CollapsingToolbarLayout
        
        <com.google.android.material.appbar.MaterialToolbar
            ...
            android_layout_height="?attr/actionBarSize"
         
         <include
            ... 
            android_layout_marginTop="?attr/actionBarSize"
         
...

I am trying to include a layout under the toolbar within a CollapsingToolbarLayout.
The first draft was without the linearlayout, but doing so the toolbar was overlapping the included layout.
So I put the toolbar and the layout into a linearlayout. The layout is under the toolbar as intended, but the scrolling behaviour is now gone.
They just stay at the same place and don’t scroll.

<com.google.android.material.appbar.AppBarLayout
        android_id="@+id/appbar"
        android_layout_width="match_parent"
        android_layout_height="wrap_content"
        android_fitsSystemWindows="true"
        app_liftOnScroll="true">
<com.google.android.material.appbar.CollapsingToolbarLayout
            android_id="@+id/toolbar_layout"
            style="@style/Widget.SaltWatcher.App.Toolbar"
            android_layout_width="match_parent"
            android_layout_height="wrap_content"
            app_layout_scrollFlags="scroll|exitUntilCollapsed"
            app_titleEnabled="false"
            app_toolbarId="@id/toolbar">

            <LinearLayout
                android_layout_width="match_parent"
                android_layout_height="wrap_content"
                android_orientation="vertical"
                app_layout_collapseMode="pin"
                app_layout_scrollFlags="scroll|exitUntilCollapsed">

                <com.google.android.material.appbar.MaterialToolbar
                    android_id="@+id/toolbar"
                    style="@style/Widget.SaltWatcher.App.Toolbar"
                    android_layout_width="match_parent"
                    android_layout_height="?attr/actionBarSize"
                    android_elevation="0dp"
                    app_contentInsetStart="0dp"
                    app_elevation="0dp"
                    app_layout_collapseMode="parallax" />

                <include
                    android_id="@+id/values"
                    layout="@layout/layout_values"
                    android_layout_width="match_parent"
                    android_layout_height="136dp"
                    android_layout_gravity="bottom"
                    android_scaleType="centerCrop"
                    app_contentInsetStart="0dp"
                    app_layout_collapseMode="parallax" />
            </LinearLayout>
        </com.google.android.material.appbar.CollapsingToolbarLayout>
    </com.google.android.material.appbar.AppBarLayout>