Use shared inference-result constants instead of raw strings in responses.py

[coderabbitai]

Summary

In src/app/endpoints/responses.py, the raw string literals "success" and "failure" are passed to _record_response_inference_result in multiple places. Since src/metrics/recording.py already exports LLM_INFERENCE_RESULT_SUCCESS and LLM_INFERENCE_RESULT_FAILURE constants for exactly this purpose, the raw literals should be replaced with these constants to reduce typo risk and prevent silent metric skew.

Affected locations

• Around line 1045–1052 (streaming path — terminal event handling in response_generator)
• Around lines 1188–1193 (non-streaming path — success recording in handle_non_streaming_response)
• Around lines 1222–1225 (non-streaming path — failure recording in handle_non_streaming_response)

Suggested fix

-                result = "failure" if chunk.type == "response.failed" else "success"
+                result = (
+                    recording.LLM_INFERENCE_RESULT_FAILURE
+                    if chunk.type == "response.failed"
+                    else recording.LLM_INFERENCE_RESULT_SUCCESS
+                )

Apply the same substitution to the other two occurrences where "success" and "failure" are passed directly.

References

• PR: RSPEED-2943: add Responses API inference metrics #1641
• Review comment: RSPEED-2943: add Responses API inference metrics #1641 (comment)
• Requested by: @tisnik