I found no notification from chat room and never know if someone replied in chat room.
Is it possible to have notification from chat room just like the badge showing up when other leaving comment in question?
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If they refer to your name, as it is possible to do in comments, then you get a notification, but only if you visited the chat in the past days. (I don't recall how much days.)
For what I have experienced, those notifications are sometimes not delivered, but this must be an underlying bug.