I need to go back and revise it a bit, but I built a bit of UI for doing just this with Webmention: https://boffosocko.com/2017/12/24/adding-simple-twitter-response-buttons-to-wordpress-posts/
The other piece requires being able to thread conversations. Details for that here: https://boffosocko.com/2018/07/02/threaded-conversations-between-wordpress-and-twitter/