The football team I support have an unofficial fan forum which still runs on an antiquated (but maintained) Perl based e-Blah system and is very active.
A few others include RailForums (https://railforums.co.uk/) which runs on more modern forum software and the Monzo Community (https://community.monzo.com/)
Isn't Hacker News technically a forum too, just a bit more bespoke & for lack of better words, reddit-y?
I think the main distinction between "forums" and "Reddit/HN/FB/Twitter" is that when posting on a forum that thread goes up to the top of the "feed", i.e. threads are sorted in chronological order by latest activity.
On Reddit/HN/FB/Twitter threads tend to die over time, due to the algorithms. On Reddit discussion literally dies after 6 months when a post is locked. On Twitter on the other hand old "threads" can be resurrected by activity or retweeting but yeah, it's nothing resembling a forum, one of which strengths is the ability to maintain threads running actively for multiple years.
So in conclusion I'd say HN is somewhat in-between. There's no notifications for replies built-in, but there is https://hnreplies.com/ so essentially it's possible to maintain an active thread (between the participants who receive notifications) but there won't be any new users discovering the discussion taking place.