Context: a custom plugin

My goal: i need to redirect user to another site after a logout 

I wrote these 

    error_log("test of error logging");

    add_action('wp_logout', function () {
      error_log("do_action wp_logout_called");
    });
    
    add_action('wp_logout', function()
      {
        wp_redirect('https://www.google.it');
        exit();
      };

In the error_log i can see test of error logging, so plugin is loaded and error logging works

But
1. I never see `do_action wp_logout_called`, never logged at all
2. The redirect is not working (the user returns to wordpress, no error, no redirect)

What am I doing wrong?

Edit 1 - More trial
-

I tried a manual logut using 

    http://www.domain.ext/wp-login.php?action=logout&redirect_to=https%3A%2F%2Fwww.google.it&_wpnonce=a7b9f2e2b0

Esit: logout works, but i'm redirected to home page.