Truth is we don't know that the subdomain got leaked. The example user agent they give says that the methodology they're using is to scan the IPv4 space, which is a great example of why security through obscurity doesn't work here: The IPv4 space is tiny and trivial to scan. If your server has an IPv4 address it's not obscure, you should assume it's publicly reachable and plan accordingly.

> Subdomains can be passwords and a well crafted subdomain should not leak, if it leaks there is a reason.

The problem with this theory is that DNS was never designed to be secret and private and even after DNS over HTTPS it's still not designed to be private for the servers. This means that getting to "well crafted" is an incredibly difficult task with hundreds of possible failure modes which need constant maintenance and attention—not only is it complicated to get right the first time, you have to reconfigure away the failure modes on every device or even on every use of the "password".

Here are just a few failure modes I can think of off the top of my head. Yes, these have mitigations, but it's a game of whack-a-mole and you really don't want to try it:

* Certificate transparency logs, as mentioned.

* A user of your "password" forgets that they didn't configure DNS over HTTPS on a new device and leaves a trail of logs through a dozen recursive DNS servers and ISPs.

* A user has DNS over HTTPS but doesn't point it at a server within your control. One foreign server having the password is better than dozens and their ISPs, but you don't have any control over that default DNS server nor how many different servers your clients will attempt to use.

* Browser history.

Just don't. Work with the grain, assume the subdomain is public and secure your site accordingly.