"update_url": "https://localhost:44382/updates.xml"

<?xml version='1.0' encoding='UTF-8'?>
<gupdate xmlns='http://www.google.com/update2/response' protocol='2.0'>
  <app appid='aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa'>
    <updatecheck codebase='https://localhost:44382/extension.crx' version='2.0' />
  </app>
</gupdate>