title: Changing shipping fields values in WooCommerce doesn't work
body: <p>In my WooCommerce store I have an external API with the map for picking shipping address. After user choose place of delivery on the map, shipping address is send from client to server using AJAX.</p>
  <p>Here's my Javascript functions invoked every time user change shipping address:</p>
  <pre><code>const changeShippingAddress = (address, postalCode, city) =&gt; {
      wp.ajax.post( &quot;change_shipping_address&quot;, {
          address,
          postalCode,
          city
      } )
          .done(function(response) {
              alert(response);
          })
          .fail(err =&gt; {
              alert(&quot;fail&quot;);
              alert(err);
          });
  }
  </code></pre>
  <p>And here's my PHP code in <code>functions.php</code>:</p>
  <pre><code>add_action( 'wp_ajax_nopriv_change_shipping_address', 'mytheme_change_shipping_address' );
  add_action( 'wp_ajax_change_shipping_address', 'mytheme_change_shipping_address' );
  
  function mytheme_change_shipping_address() {
      WC()-&gt;customer-&gt;set_shipping_address($_POST['address']);
      WC()-&gt;customer-&gt;set_shipping_postcode($_POST['postalCode']);
      WC()-&gt;customer-&gt;set_shipping_city($_POST['city']);
  
      wp_send_json_success('success');
  }
  </code></pre>
  <p>Values are sending properly from client to server with AJAX (I can read them on server side and send them back to client with <code>wp_send_json_success</code>), but the problem is, shipping fields aren't updated (after sending form, error about empty shipping fields shows up). Why is that happened? Is something wrong with my <code>set_shipping</code> functions?</p>