The "Marketing Channel Detail" value is populated by the processing rules for the Marketing Channel Report in the admin console. When configuring a rule, you set the criteria for defining how a hit will be bucketed into a channel, and in that same rule, you define what the "Marketing Channel Detail" value will be. This is not driven by classifications. I've included a screenshot here.
![Screenshot 2024-02-13 at 10.31.55 AM.png Screenshot 2024-02-13 at 10.31.55 AM.png](https://experienceleaguecommunities.adobe.com/t5/image/serverpage/image-id/70045i8F97549C7A2D6D44/image-size/medium?v=v2&px=400)
You also have many options as to what the value is, such as a query parameter, referring domain/url, etc.
EDIT: Also including a reference to the documentation here: https://experienceleague.adobe.com/docs/analytics/admin/admin-tools/manage-report-suites/edit-report...