ENH: easy access to raw response

In recent debugging sessions it became painful that the multiple inheritances and layered methods makes e.g. accessing the raw response more difficult than necessary.

So, while a full refactoring and simplification could be a huge project, giving access to the raw response could be a nice and reasonably quick enhancement.

cc @andamian and @tomdonaldson

The issue names no files, classes, or tests. Start by tracing the layered response and service methods that handle remote requests, then identify where the raw response is available and how existing callers expose related data. Done means a documented, direct way to access that raw response without undertaking the broader inheritance refactoring.

Written by the indexing model from the issue text.