Additionally, how would Cohen know to execute an agreement and with who?
That is not logical. When people try & contact DJT they are referred to the proper person, who would have been Cohen for legal matters. SD would never have gotten to DJT for conversation on a this subject or probably any subject, that’s what secretaries are for.
The agreement would have been with Cohen as an ongoing thing for all legal matters of a defined type. Depending on the material in any given time period the charges would have varied. It is very reasonable that the bills were just paid.