When creating and saving a CoBrowse Call, the Call Type does not switch to note that it is a Detail Call. It is still Call Only.
This is by design. The Call Type is controlled by Call Attributes.
Example: Product Details or Samples.
CoBrowse Call Reports always remain Call Only unless the Product Details are explicitly selected in the Call Report. CoBrowse does not modify Call Type picklist behavior.
This works as designed.
CRM Help Documentation: Components of Call Reporting