Currently, updating Slack settings to add notifications in the channel if the assignee field is updated doesn't update the truncated notification when the assignee is changed, instead, it fires a new notification. 

The suggestion is to update the truncated notification instead of firing a new one.

WorkAround:

A workaround to have something similar is by changing the assignee from the original notification itself and removing the 2nd notification. This will update the response in a thread.