This may be because you have sent the emails from your management dashboard and not directly from one of your Applications. The Client ID used when you Send/“Try” the emails from dashboard is a generic application called “All Applications” that will not show up in the Application list.
“home_url” and “support_url” are the same. They can be configured in your tenant settings under Support URL: https://manage.auth0.com/#/tenant
Hope this helps.