The error mysteriously disappeared and was replaced by an authentication error. I managed to have my Postmark account unlocked (btw, their support team was way much better than that of Sendgird, which still hasn't responded for 2 days since I requested till I am typing right now) and found that to use Postmark in Nodemailer you have to set the server api token as both the username and the password. This is quite counter intuitive, in my opinion.

And I finally figured out that, the test email button works on your last saved settings, not what you are editing in the input boxes right now.

So now Postmark is working. Thank God.

@Meketeke I think removing Cloudflare as proxy or DNS manager was not the solution as it defied the whole reason and purpose you tried to use Cf in the first place (which are the anti DDoS and other stuff). The solution was quite simple as @julian pointed out, the url in the config.json should match the setting in whatever reverse proxy you are using on the machine (say it NginX). If you are like me who is not using https in NginX since Cloudflare already does that, then the url in your config.json should be something like http://yourdomain.com, instead of https://yourdomain.com as one may first suppose.

At least that's how I solved the very same problem yesterday.