exclude by URL

The issest way is to hide the search conditionally via CSS. Here is PHP snippet you can apply.

add_action( 'wp_head', function () {
  $r = $_SERVER['REQUEST_URI'];

  if ( ! empty( $r ) && strpos( $r, '/negozio/' ) !== false ) {
    ?>
    <style>
      .dgwt-wcas-widget {
        display: none;
      }
    </style>
    <?php
  }
} );

You have two ways to add this code to your theme:

Open the functions.php in your Child Theme and add the code at the end
or install the Code Snippets plugin and apply this code as a snippet

Best
Damian

works perfectly, thanks.
Because the site has a second language, I’m sure I can duplicate the snippet changing the name of the page, but there is a way to include both pages in the same code so to avoid having two snippets doing the same??
that’s the ENG url
https://www.mercatodeivignaioli.it/en/shop/

Ok, I wrote a code. Thanks

Then use it:

add_action( 'wp_head', function () {
  $r = $_SERVER['REQUEST_URI'];

  if ( ! empty( $r ) &&
       ( strpos( $r, '/negozio/' ) !== false || strpos( $r, '/en/shop/' ) !== false )
     ) {
    ?>
    <style>
      .dgwt-wcas-widget {
        display: none;
      }
    </style>
    <?php
  }
} );