AFAIK (at least it worked like that some 10 years ago) the captive portal just intercepts the HTTP page load and inserts its own content (most often a 302). So it just has to be a http web page. Firefox uses http://detectportal.firefox.com/canonical.html

Relevant support page, though light in details: https://support.mozilla.org/en-US/kb/captive-portal

Edit: ah, yes, DNS can be hijacked too (requires intercepting outgoing traffic on port 53 therefore incompatible with DoH), that may require fewer computing resources. Still need http otherwise the server cannot use the correct cert chain.

Edit 2: Wikipedia says both methods are used: https://en.wikipedia.org/wiki/Captive_portal and also mentions RFC 8910. I suspected something like that existed, hence my initial disclaimer.

My point was: that domain is not treated any differently from other domains.

Can we take a minute to appreciate how utterly broken this state of affairs is? The dogged over centralization of DNS is an endless source of problems.