How to insert Collate into WordPress search query?

You should add the following code to the functions.php of your theme (and it is better to make all modifications in child theme):

add_filter( 'posts_search' , 'posts_search' );
function posts_search( $search ) {
    $search = str_replace( 'LIKE', 'COLLATE utf8_bin LIKE', $search );

    return $search;
}

It works. You can check it on my test site:

http://test.kagg.eu/?s=čėšū

returns one post, but

http://test.kagg.eu/?s=cesu

returns nothing.