Thanks for clarifying!
The user’s email will be verified only after they reset their password when mark_email_as_verified is true.
When you call the /api/v2/tickets/password-change endpoint, you will receive a URL that can be used in a template in your own external email provider. You can use the Post-User Registration Hook to trigger the email.
Here is an example of sending an email in a Rule with the Mandrill email provider: Auth0 Actions. You could do something similar in a Post-User Registration Hook to send the email.
You can also follow this answer to use the Auth0 change password email template: Sending password change email instead of verification email for a new user - #3 by stephanie.chamblee
With this solution, you would likely need to configure the template in a way that regular password change requests would look different than the initial password reset.