I have configured SMTP and the postpone extended email step. Jenkins is white listed, so I do not need to specify the credentials.
Job finishes successful. But why it does not sends anything?
Second problem. I had some "successful" ext. email step runs with "no emails were triggered" result.
Check what triggers a sending email.
I'm not sure if your second printscreen contains all configuration. But there I can see that only "Any failure" triggers sending email. So if job finished successfully no email were sent.