Show woocommerce products in author archive

Use pre_get_posts to modify author archive queries-

function wpd_author_archive( $query ){
    if ( $query->is_author() && $query->is_main_query() ){
        $query->set( 'post_type', array( 'post', 'product' ) );
    }
}
add_action( 'pre_get_posts', 'wpd_author_archive' );