fix(logging): capture streaming TTFB on first chunk and make timestamps required

- Add firstChunkTimestamp field to ResponseWriterWrapper for sync capture
- Capture TTFB in Write() and WriteString() before async channel send
- Add SetFirstChunkTimestamp() to StreamingLogWriter interface
- Make requestTimestamp/apiResponseTimestamp required in LogRequest()
- Remove timestamp capture from WriteAPIResponse() (now via setter)
- Fix Gemini handler to set API_RESPONSE_TIMESTAMP before writing response

This ensures accurate TTFB measurement for all streaming API formats
(OpenAI, Gemini, Claude) by capturing timestamp synchronously when
the first response chunk arrives, not when the stream finalizes.

sdk/api/handlers/gemini/gemini-cli_handlers.go

@@ -124,8 +124,8 @@ func (h *GeminiCLIAPIHandler) CLIHandler(c *gin.Context) {
 			log.Errorf("Failed to read response body: %v", err)
 			return
 		}
-		_, _ = c.Writer.Write(output)
 		c.Set("API_RESPONSE_TIMESTAMP", time.Now())
+		_, _ = c.Writer.Write(output)
 		c.Set("API_RESPONSE", output)
 	}
 }