I believe it's a new update, for me it's cool for my site. Also they are not private conversation as you put it. They drawn from general comments on post referencing the post itself. I find this interesting though.

To solve this if you don't want this, go studio->timeline->general-> and unmarked the untranslated key "_bx_timeline_alert_module_comment (add)" then save. Clear cache and you should be fine.

Also in addition, I would like to propose that not all comments should be served as a new post, perhaps it's better a settings can be added, say for comment trend, if a comment has "n" replies, then the comment will be served as a new created post. Also, conversations in conversation module shouldnot appear. Boon Alex T⚜️