Support server-side conversation history on responses API

[jaredoconnell]

Summary

Add support for server-side conversation history via previous_response_id on the /v1/responses endpoint. This allows multi-turn benchmarks to offload conversation state to the server instead of replaying the full history in every request, which is critical for benchmarking servers that use response storage (e.g. vLLM with VLLM_ENABLE_RESPONSES_API_STORE=1).

Details

• Add server_history option to OpenAIHTTPBackend, validated to only work with /v1/responses
• Update ResponsesRequestHandler.format() to set previous_response_id from the prior response instead of replaying history when server_history is enabled.
• Add unit tests for validation and request formatting with server_history
• Document server-side history usage and requirements in docs/guides/multiturn.md

Test Plan

• Run pytest tests/unit/backends/openai/test_http.py -k server_history
• Run pytest tests/unit/backends/openai/test_request_handlers.py -k server_history
• (Integration) Against a vLLM server with VLLM_ENABLE_RESPONSES_API_STORE=1, run a multiturn benchmark with --request-format /v1/responses --backend-kwargs '{"server_history": true}' and confirm turn 2+ requests use previous_response_id

---

• "I certify that all code in this PR is my own, except as noted below."

Use of AI

• Includes AI-assisted code completion
• Includes code generated by an AI application
• Includes AI-generated tests (NOTE: AI written tests should have a docstring that includes ## WRITTEN BY AI ##)

[sjmonson]

LGTM