[CI] Add E2E tests for Response API

[Xunzhuo]

Summary

Add end-to-end tests for the Response API to ensure the complete request/response flow works correctly through Envoy and the semantic-router extproc.

Background

PR #802 introduced Response API support. E2E tests are needed to validate:

• Request translation from Response API to Chat Completions
• Response translation back to Response API format
• Path rewriting (/v1/responses → /v1/chat/completions)
• Conversation chaining with previous_response_id
• All CRUD endpoints work correctly

Test Scenarios

Basic Operations

• POST /v1/responses - Create a new response
• GET /v1/responses/{id} - Retrieve a response
• DELETE /v1/responses/{id} - Delete a response
• GET /v1/responses/{id}/input_items - List input items

Translation Tests

• Verify request body is correctly translated to Chat Completions format
• Verify response body is correctly translated to Response API format
• Verify :path header is rewritten to /v1/chat/completions
• Verify content-length is recalculated after body mutation

Conversation Chaining

• Create initial response, verify ID is returned
• Create follow-up with previous_response_id
• Verify conversation history is included in backend request
• Test chain of 3+ responses

Error Handling

• Invalid request format (missing input field)
• Non-existent previous_response_id
• Non-existent response ID for GET/DELETE
• Backend error passthrough

Edge Cases

• Empty input
• Large input (token limit)
• Special characters in input
• Concurrent requests

Test Infrastructure

• Set up test Envoy config with Response API enabled
• Mock or stub vLLM backend for consistent responses
• Add to CI pipeline

Related

• Parent PR: [Feat][Memory] Add OpenAI Response API support #802
• Config example: config/testing/config.response-api.yaml