The problem:
Currently, there is no way to see how mappers are executed on extract, and what data was passed after transformation. The same for $populate - there's no way to see how source queries were executed.
Possible solutions:
For $extract add param ?__debug=True that will add an extra field into the response with data that was sent to FHIR Server.
For $populate add param ?__debug=True that will add an extra field into the response with source queries that were executed