Simplify mocking of client libraries for customers

We talked a while back about doing something like the Azure SDK for Go, but I wonder if in the meantime we could expose our mock `HttpClient` from the unpublished (by design) `azure_core_test` crate instead, perhaps, in the `azure_core/test` feature. We'd probably want to clean it up some and have a serious design review.

_Originally posted by @heaths in [#1874](https://github.com/Azure/azure-sdk-for-rust/issues/1874#issuecomment-2870753398)_