How do I add a custom body class to the admin area of a page?

Use admin_body_class both with global post_id and get_current_screen function:

add_filter('admin_body_class', 'wpse_320244_admin_body_class');

function wpse_320244_admin_body_class($classes) {
    global $post;

    // get_current_screen() returns object with current admin screen
    // @link https://codex.wordpress.org/Function_Reference/get_current_screen
    $current_screen = get_current_screen();

    if($current_screen->base === "post" && absint($post->ID) === 8) {
        $classes .= ' home-admin-area';
    }

    return $classes;
}

You can also use $pagenow variable. It seems that this way would be preferable, because get_current_screen() maybe undefined in some cases:

add_filter('admin_body_class', 'wpse_320244_admin_body_class');

function wpse_320244_admin_body_class($classes) {
    global $post, $pagenow;

    // $pagenow contains current admin-side php-file
    // absint converts type to int, so we can use strict comparison
    if($pagenow === 'post.php' && absint($post->ID) === 8) {
        $classes .= ' home-admin-area';
    }

    return $classes;
}