You can leave the query variable, although it should use $wpdb->prepare
https://developer.www.ads-software.com/reference/classes/wpdb/prepare/
and then instead of mysql_query or mysql_fetch it needs to be the corresponding method of $wpdb. It’s best just to use the wrapper functions that do what the code is trying to do like get_post_meta.

$sql = $wpdb->prepare( "SELECT value FROM wp_acf_values WHERE wp_acf_values.field_id = '105' AND wp_acf_values.id = '234'" );
          $result = $wpdb->query ( $sql ) or die('Content was not loaded. Please refresh your page.');
          while($post = mysql_fetch_array($result)) {

            $sqlTitle = $wpdb->prepare( "SELECT meta_value FROM wp_postmeta WHERE meta_id = %s", $post['value'] );
            $result1 = $wpdb->query ( $sqlTitle ) or die('Content was not loaded. Please refresh your page.');
            while($post1 = mysql_fetch_array($result1)) {
              $spotlightTitle = $post1['meta_value'];
            }

          }

<?

global $wpdb;

$sql = $wpdb->prepare( "SELECT value FROM wp_acf_values WHERE wp_acf_values.field_id = '105' AND wp_acf_values.id = '234'" );
$result = $wpdb->query ( $sql ) or die('Content was not loaded.');

while($post = mysql_fetch_array($result)) {

$sqlTitle = $wpdb->prepare( "SELECT meta_value FROM wp_postmeta WHERE meta_id = %s", $post['value'] );
$result1 = $wpdb->query ( $sqlTitle ) or die('Content was not loaded.');
     while($post1 = mysql_fetch_array($result1)) {
        $spotlightTitle = $post1['meta_value'];
     }
}
?>

If you look at the docs you’ll see that none of the wpdb methods return a mysql results object, or any mysql objects at all, and none of the examples use mysql functions.

e.g.

$fivesdrafts = $wpdb->get_results( 
	"
	SELECT ID, post_title 
	FROM $wpdb->posts
	WHERE post_status = 'draft' 
		AND post_author = 5
	"
);

foreach ( $fivesdrafts as $fivesdraft ) 
{
	echo $fivesdraft->post_title;
}