Sent emails not logged in 'Past Activity' after Einstein Activity Capture is activated

Enabling Einstein Activity Capture changes the way the Lightning 'Activity Timeline' functions.  With Einstein Activity Capture enabled, Emails sent via an Account record are ONLY added to 'Past Activity' at the Account level when the following criteria are met:

1. The Email recipient is a directly related Contact.
2. The Related Contact has valid email address.

With Einstein Activity Capture enabled, Emails sent via an Opportunity record are ONLY added to 'Past Activity' at the Opportunity level when the following criteria are met:

1. The recipient's email address is associated with a Contact in the organization.
2. That Contact is added to the 'Contact Roles' related list on the Opportunity record.

In other words, Einstein Activity Capture (EAC), also referred to as Inbox, has a dependency on Contact relationships.

NOTE: Custom Object Limitaion:

Custom Objects are currently unsupported by Einstein Activity Capture.  Email sent via custom object records are logged in the Activity Timeline of the Contact that's associated with the email recipient.