Currently the only way to end a Message Session is on the list view, and "Configure Messaging" permission is required.
It should be possible to end a Message Session systematically through Apex Code and Process Builder.
This is related to two other ideas:
End Messaging Session on the Layout or List View
"End Session" should not be tied to Configure Messaging permission
|Note: As of the date of posting this 4/29/2020, I could not find a category for Messaging, the closest thing I could find is Live Agent, which is actually a different feature. The category of this could actually fall under Digital Engagement.|