> It'd be interesting to have a look at that news site forum (if you have a link?).

I doubt that you will find it particularly useful (site in Russian, and I've no idea how reliably that feature works for unregistered users), but anyway: https://www.opennet.ru/forum/

> I wonder how they determine which messages are new. Maybe it's [new since one's last visit]?

It is. While not as powerful as status tracking for individual messages (can't skip some messages for future read as easily, can't mark message as unread etc.), it is enough for most users most of the time.