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I found the key: SQL CASE Expression

add_filter( 'posts_orderby', 'order_search_by_posttype', 10, 2 );
function order_search_by_posttype( $orderby, $wp_query ){
    if( ! $wp_query->is_admin && $wp_query->is_search ) :
        global $wpdb;
        $orderby =
            "
            CASE WHEN {$wpdb->prefix}posts.post_type = 'artist' THEN '1' 
                 WHEN {$wpdb->prefix}posts.post_type = 'post' THEN '2' 
                 WHEN {$wpdb->prefix}posts.post_type = 'artwork' THEN '3' 
                 WHEN {$wpdb->prefix}posts.post_type = 'publication' THEN '4' 
            ELSE {$wpdb->prefix}posts.post_type END ASC, 
            {$wpdb->prefix}posts.post_title ASC";
    endif;
    return $orderby;
}

I found the key: SQL CASE Expression

function order_search_by_posttype($orderby){
    if (!is_admin() && is_search()) :
        global $wpdb;
        $orderby =
            "
            CASE WHEN {$wpdb->prefix}posts.post_type = 'artist' THEN '1' 
                 WHEN {$wpdb->prefix}posts.post_type = 'post' THEN '2' 
                 WHEN {$wpdb->prefix}posts.post_type = 'artwork' THEN '3' 
                 WHEN {$wpdb->prefix}posts.post_type = 'publication' THEN '4' 
            ELSE {$wpdb->prefix}posts.post_type END ASC, 
            {$wpdb->prefix}posts.post_title ASC";
    endif;
    return $orderby;
}
add_filter('posts_orderby', 'order_search_by_posttype');

I found the key: SQL CASE Expression

add_filter( 'posts_orderby', 'order_search_by_posttype', 10, 1 );
function order_search_by_posttype( $orderby ){
    if( ! is_admin() && is_search() ) :
        global $wpdb;
        $orderby =
            "
            CASE WHEN {$wpdb->prefix}posts.post_type = 'artist' THEN '1' 
                 WHEN {$wpdb->prefix}posts.post_type = 'post' THEN '2' 
                 WHEN {$wpdb->prefix}posts.post_type = 'artwork' THEN '3' 
                 WHEN {$wpdb->prefix}posts.post_type = 'publication' THEN '4' 
            ELSE {$wpdb->prefix}posts.post_type END ASC, 
            {$wpdb->prefix}posts.post_title ASC";
    endif;
    return $orderby;
}

I found the key: SQL CASE Expression

add_filter( 'posts_orderby', 'order_search_by_posttype', 10, 2 );
function order_search_by_posttype( $orderby, $wp_query ){
    if( ! $wp_query->is_admin && $wp_query->is_search ) :
        global $wpdb;
        $orderby =
            "
            CASE WHEN {$wpdb->prefix}posts.post_type = 'artist' THEN '1' 
                 WHEN {$wpdb->prefix}posts.post_type = 'post' THEN '2' 
                 WHEN {$wpdb->prefix}posts.post_type = 'artwork' THEN '3' 
                 WHEN {$wpdb->prefix}posts.post_type = 'publication' THEN '4' 
            ELSE {$wpdb->prefix}posts.post_type END ASC, 
            {$wpdb->prefix}posts.post_title ASC";
    endif;
    return $orderby;
}

I found the key: SQL CASE Expression

add_filter( 'posts_orderby', 'order_search_by_posttype', 10, 2 );
function order_search_by_posttype( $orderby ){
    global $wpdb;
    if( ! is_admin() && is_search() ) :
    $orderby =
        "CASE WHEN {$wpdb->prefix}posts.post_type = 'artist' THEN '1' 
              WHEN {$wpdb->prefix}posts.post_type = 'post' THEN '2' 
              WHEN {$wpdb->prefix}posts.post_type = 'artwork' THEN '3' 
              WHEN {$wpdb->prefix}posts.post_type = 'publication' THEN '4' 
              ELSE {$wpdb->prefix}posts.post_type END ASC, 
        {$wpdb->prefix}posts.post_title ASC";
    endif;
    return $orderby;
}

I found the key: SQL CASE Expression

add_filter( 'posts_orderby', 'order_search_by_posttype', 10, 1 );
function order_search_by_posttype( $orderby ){
    if( ! is_admin() && is_search() ) :
        global $wpdb;
        $orderby =
            "
            CASE WHEN {$wpdb->prefix}posts.post_type = 'artist' THEN '1' 
                 WHEN {$wpdb->prefix}posts.post_type = 'post' THEN '2' 
                 WHEN {$wpdb->prefix}posts.post_type = 'artwork' THEN '3' 
                 WHEN {$wpdb->prefix}posts.post_type = 'publication' THEN '4' 
            ELSE {$wpdb->prefix}posts.post_type END ASC, 
            {$wpdb->prefix}posts.post_title ASC";
    endif;
    return $orderby;
}