feat(logging): add timestamp to API RESPONSE section in error logs

[sususu98]

Summary

• Add timestamp to the === API RESPONSE === section header in error logs
• Timestamp is captured when the API response is received (not when the log is written)
• Enables diagnosis of slow backend responses by comparing with request timestamp

Example Output

=== REQUEST INFO ===
Timestamp: 2026-01-27T18:18:30.366575728+08:00
...

=== API RESPONSE === (Timestamp: 2026-01-27T18:19:45.123456789+08:00)
{...response...}

The time difference between these timestamps shows actual backend response latency.

[gemini-code-assist]

Summary of Changes

Hello @sususu98, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request introduces a significant improvement to the logging infrastructure by embedding timestamps directly into the 'API RESPONSE' section of error logs. This enhancement provides a clear, real-time marker of when an API response was received, which is invaluable for pinpointing and analyzing backend latency issues. The changes are implemented consistently across both non-streaming and streaming log writers, ensuring that critical timing information is always available for performance diagnostics.

Highlights

• Timestamping API Responses: The logging system now includes a timestamp in the '=== API RESPONSE ===' section header for error logs. This timestamp is captured precisely when the API response is received, not when the log entry is written.
• Enhanced Latency Diagnosis: By comparing the newly added API response timestamp with the existing request timestamp, developers can accurately diagnose and measure backend response latency, aiding in performance analysis.
• Refactored Logging Function: The writeAPISection function has been modified to accept an optional time.Time parameter. If provided and non-zero, this timestamp is formatted and appended to the section header.
• Streaming Log Support: For streaming logs, a new field apiResponseTimestamp was added to the FileStreamingLogWriter struct to store the response reception time, ensuring consistent timestamping across different logging scenarios.

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[gemini-code-assist]

Code Review

The pull request successfully implements the feature to add a timestamp to the === API RESPONSE === section in error logs. The timestamp is correctly captured when the API response is received and formatted using time.RFC3339Nano for precision. The changes are well-contained and logically applied to both non-streaming and streaming log writers. The code is clean and adheres to Go best practices.

[sususu98]

Superseded by #1300 with improved implementation:

• Fixed REQUEST INFO timestamp (now captured at request arrival, not log write time)
• Fixed API RESPONSE timestamp (now captured when response arrives, not at log write time)