This function adds product SKUs to the default WordPress search.

/* adding SKUs to default WP search BEGIN */
function search_by_sku( $search, $query_vars ) {
    global $wpdb;
    if(isset($query_vars->query['s']) && !empty($query_vars->query['s'])){
        $args = array(
            'posts_per_page'  => -1,
            'post_type'       => 'product',
            'meta_query' => array(
                array(
                    'key' => '_sku',
                    'value' => $query_vars->query['s'],
                    'compare' => 'LIKE'
                )
            )
        );
        $posts = get_posts($args);
        if(empty($posts)) return $search;
        $get_post_ids = array();
        foreach($posts as $post){
            $get_post_ids[] = $post->ID;
        }
        if(sizeof( $get_post_ids ) > 0 ) {
                $search = str_replace( 'AND (((', "AND ((({$wpdb->posts}.ID IN (" . implode( ',', $get_post_ids ) . ")) OR (", $search);
        }
    }
    return $search;
    
}
add_filter( 'posts_search', 'search_by_sku', 999, 2 );
/* adding SKUs to default WP search END */