[Test-Proxy] Enable skip recording request bodies

[catalinaperalta]

Leverage changes implemented in this PR to allow not recording request bodies: Azure/azure-sdk-tools#2692

[github-actions]

Hi @catalinaperalta, we deeply appreciate your input into this project. Regrettably, this issue has remained inactive for over 2 years, leading us to the decision to close it. We've implemented this policy to maintain the relevance of our issue queue and facilitate easier navigation for new contributors. If you still believe this topic requires attention, please feel free to create a new issue, referencing this one. Thank you for your understanding and ongoing support.

[mccoyp]

@catalinaperalta, sorry I didn't get to this feature! I can open another tracking issue if this request is still relevant. Is this still relevant after moving recordings out of the Python repository? (I ask because other languages omitted this feature since it was intended to save repo space.)

[catalinaperalta]

Hi @mccoyp, this issue was affecting the old form recognizer SDK recordings, but we've since moved on to the new document intelligence SDK which didnt seem to have an issue with new recordings, so we can keep this closed and see if it becomes relevant for any new SDK in the future and open an issue then.