[PD][OpenAI] Gate /v1/responses persistence behind --enable-response-store, default off (#39122)

Co-authored-by: Xinyuan Tong <xinyuantong.cs@gmail.com>

docs/docs/advanced_features/server_arguments.mdx

@@ -1063,6 +1063,16 @@ Please consult the documentation below and [server_args.py](https://github.com/s
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+## Responses storage
+
+Responses storage is now disabled by default, including on standalone servers. Add `--enable-response-store` to retain responses for retrieval, `previous_response_id` chaining, and background requests. Storage is process-local and in-memory, has no TTL or size limit, and is lost on restart.
+
+Foreground generation and streaming still accept the API's default `store: true` without retaining responses or message history when server storage is disabled. The response's `store` field echoes the client request; the server flag controls persistence. With storage enabled, `store: false` opts out for the current request while allowing it to read a stored predecessor.
+
+Background requests, including streaming requests, require both `--enable-response-store` and `store: true`. Without the flag, chaining, background requests, retrieval, and cancellation return HTTP 400. Cancellation applies to detached background requests; active streams have no stored response until completion.
+
+Combining `--enable-response-store` with `--disaggregation-mode=prefill` or `decode` fails at startup. PD clients must send explicit conversation history in foreground requests. Built-in web search and code interpreter calls are also unsupported under PD.
+
 ## API related
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