I've been thinking that I should 'break out' that feature as a Chrome extension. It would open the Twitter discussion for the link you're on, as a sidebar. Here's an image of how the sidebar would look (this is a sample of tweets about a particular article called 'Podcasting's Next Frontier'): https://imgur.com/a/GEcR7b1
And if that Chrome extension becomes popular maybe I would ditch the dependence on Twitter and also spider the rest of the web for discussions about the URL, especially big forums like HN, Reddit. I think https://techmeme.com does something like that.
As an aside, this is the kinda thing I miss about the circa 2005 web--when there was a prominent article published it would get discussed in a variety of forums, blogs, etc. Now the discussion has become centralized to a few aggregators and social media sites.