When utilizing an automation to send an Engage message, the information will only log on the primary contact when the trigger record is a Task, Job, or Contact trigger.
This feature is absent when utilizing an automation that triggers from an Invoice, Estimate, Material Order, or Work Order and can only fully be viewed when reviewing the Engage conversation.

I would like the ability to see all my Engage activity on the primary contact record as this is the source of the phone number and the activity is logged here when an Email communication is sent.