[Responses API] Disable response store by default

[WoosukKwon]

This PR disables the response store for OpenAI Responses API.

While the response store is required for various features in Responses API (including background, cancel, and prev_response_id), it is currently not implemented properly in vllm. The current store causes a memory leak and is not persistent (i.e., the stored responses are lost when the server shuts down). Therefore, until we have a proper implementation, we disable this feature and only enable it under the VLLM_ENABLE_RESPONSES_API_STORE=1 env flag.

[github-actions]

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[gemini-code-assist]

Code Review

This pull request correctly disables the response store by default to prevent memory leaks, controlled by a new environment variable. The changes are well-implemented across the codebase, including tests and configuration. I have one suggestion to improve API consistency by adjusting an HTTP status code for a new error response.