Sure, we do. I'm planning to have reddit-like forums for each book over 500 ratings at the bottom of the page like IMDB used to do. Also, I'm considering forums for genres like romance, fantasy.

Forums per book is a good start, but I find that the groups are a bigger draw in Goodreads. They have a more personal touch and allow you to discuss broader topics and get recommendations from accounts you know and trust. For example I'm in a group called "Evolution of science fiction" and have learnt a lot from joining in their monthly novel / short story reads.

Do users create and moderate the group themselves? It seems like a subreddit, but for book related topics?

Yep, each group has one or more moderators. Like Reddit I guess but no up/downvotes. There's some automated moderation as well - it doesn't let you post links (which is mad) and I read that at one point there was a censoring of mentions of Storygraph.