The new Forgetful browsing feature (like the extension Cookie AutoDelete) is still new and they are rolling it slowly to the users. The linked domain is their server controlling the rollout. It’s plausible that the server being not reachable, the browser would disable the feature (debatable but ok).
Firefox and Chrome have the same kind of servers controlling individual settings and feature.
Update:
Chrome / Brave share the same code for controlling features. It’s called Google Finch. Obviously, Brave operates its own server for that and does not use Google ones.
The service and code are public:
https://github.com/brave/brave-variations https://griffin.brave.com/
A detailed explanation by Google Dev : https://www.youtube.com/watch?v=teSgavrweWI
Firefox “variations” is called Normandy https://wiki.mozilla.org/Firefox/Normandy/PreferenceRollout
https://gethomepage.dev