Add a custom class to awating comments

Here’s one way to add a custom .wpse-comment-awaiting-moderation comment class through the comment_class filter:

add_filter( 'comment_class', 'wpse_259326_comment_classes', 10, 5 );

function wpse_259326_comment_classes ( $classes, $class, $comment_ID, $comment, $post_id )
{
    if( 'unapproved' === wp_get_comment_status( $comment ) && is_array( $classes ) )
        $classes[] = 'wpse-comment-awaiting-moderation';

    return $classes;
}

where we used that wp_get_comment_status( $comment ) returns 'unapproved' for unappproved comments.

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