Just an update to say that users don’t use the chat at all.
It was used a lot on the previous forum software and it was a wanted feature, but in the end, it simply didn’t work.
I wouldn’t be surprised if it was because forum chatboxes on old software were always visible, inciting people to participate, whereas here on Discourse, you have to click an icon to open the chat. It’s always hidden by default, and people won’t notice it or make the “effort” to click it to read the content and interact. 
But the forum itself is in very good shape and way more active than before the migration to Discourse. 