You need to set both of these things to make it work correctly:

register_post_type( 'docs',
  array(
    'labels'        => array(
      'name'          => __( 'Documentation' ),
      'singular_name' => __( 'Documentation Page' ),
      'add_new'       => __( 'Add Documentation Page' ),
      'add_new_item'  => __( 'Add New Documentation Page' ),
      'edit_item'     => __( 'Edit Documentation Page' ),
    ),
    'public'       => true,
    'has_archive'  => true,
    'rewrite'      => array( 'slug' => 'docs' ),
    'show_in_rest' => true,
    'hierarchical' => true,
    'supports'     => array( 'title', 'editor', 'thumbnail', 'excerpt', 'page-attributes' )
  )
);

Now when you are on the Create/Edit screen for the new Post Type, you’ll see the Page Attributes area that allows you to select the Parent you’d like.