Nice! Love that you put up a demo and everything, that’s awesome. 
Unfortunately the site in question is using a ‘classic’ Genesis Framework theme, and further unfortunately, it is also making liberal use of Toolset archive templates, which cannot yet be replicated in a Site Editor/FSE theme.
I did some more playing around, and it seems to show both the Discourse replies (first) and WP comments (including the submit form!) if there’s at least 1 WP comment before posting to Discourse. But if you publish/link to Discourse right away, WP commenting disappears. I’m wondering if this is the case even in the block themes? I see you have some WP comments in the demo showing–did you add those before or after posting to Discourse?