`azure-ai-agents` and `azure-ai-projects` HTTPClient integration with OpenAI library

## Description

Compilation of punted tasks to improve integration with OpenAI official SDKS for `azure-ai-agents` and `azure-ai-projects`

- [x] Remove manual URL mapping (depends on this https://github.com/openai/openai-java/issues/660)
- [ ] Improve HttpResponse and HttpRequest body ingestion by avoiding reading the stream twice (https://github.com/openai/openai-java/issues/664)
- [x] Improve HttpRequest header mapping (https://github.com/openai/openai-java/issues/660)
- [x] Requests that are meant to timeout do not interrupt the Test Proxy continuing the recording of a response (See related PR #47416)
- [x] Reproduce [the changes](https://github.com/Azure/azure-sdk-for-java/pull/47416) to for the `HttpClient` in the `azure-ai-agents` into the `azure-ai-projects` folder.
- [ ] Map all OpenAI's timeout values to Azure.Core provide HttpClient request via `Context`. Related issue: #47552