What you are looking for is the excerpt (also called short description) and it’s not stored as a meta value. It’s stored with the post in the post_excerpt
column.
So you can try something like this :
// Update product with id = 44
$my_post = array(
'ID' => 44,
'post_excerpt' => 'New text',
);
// Update the post into the database
wp_update_post( $my_post );