I did some testing and more research on this topic. As you have found, the https://{yourAuth0Tenant}/api/v2/tickets/password-change will generate a ticket that contains a link to the change password page. Your application will need to send the email to the user because Auth0 does not have an API to send an email containing the ticket link.
If you look for ways to send the change password email to users, please call the POST dbconnections/change_password endpoint.
I found this feedback regarding Send Email Invitations for Application Signup. Please click on the Vote button if it addresses your concern.
Thanks!