This seems to be the standard behavior when the Contact form plugin is used on a WP site.

Currently digging in this thread to find a way to activate it only when needed as I agree it is
quite intrusive to have the recaptcha javascript code loaded on each page.

Ok, found a way by executing this in functions.php from our custom WP theme.

// load Google Recaptcha v3 only when required
add_action('wp_print_scripts', function () {
  if (!is_page(array('contact'))) {
    wp_dequeue_script('google-recaptcha');
  }
});

Fixed and deployed.