In a sense, publishing a research paper is part of an ongoing public discussion, in reply to all the other authors cited in your work.

Apart from that, there are talks at conferences which are open to discussion with the audience.

I suppose there's not really a need for much more than that, in the public sphere. There is plenty of private discussion amongst one's peers of course.

Are you referring to systems like PubPeer and PubMed Commons?

(Note: a New Zealand company in this field spammed me to get me to sign up, so that was an immediate "no" to wanting to even name them.)

FWIW, I thought there was already a lot of public discussions among academics.