perf(后端): 完成性能优化与连接池配置

新增 DB/Redis 连接池配置与校验，并补充单测

网关请求体大小限制与 413 处理

HTTP/req 客户端池化并调整上游连接池默认值

并发槽位改为 ZSET+Lua 与指数退避

用量统计改 SQL 聚合并新增索引迁移

计费缓存写入改工作池并补测试/基准

测试: 在 backend/ 下运行 go test ./...

backend/internal/service/usage_service.go

@@ -186,22 +186,40 @@ func (s *UsageService) GetStatsByApiKey(ctx context.Context, apiKeyID int64, sta
 
 // GetStatsByAccount 获取账号的使用统计
 func (s *UsageService) GetStatsByAccount(ctx context.Context, accountID int64, startTime, endTime time.Time) (*UsageStats, error) {
-	logs, _, err := s.usageRepo.ListByAccountAndTimeRange(ctx, accountID, startTime, endTime)
+	stats, err := s.usageRepo.GetAccountStatsAggregated(ctx, accountID, startTime, endTime)
 	if err != nil {
-		return nil, fmt.Errorf("list usage logs: %w", err)
+		return nil, fmt.Errorf("get account stats: %w", err)
 	}
 
-	return s.calculateStats(logs), nil
+	return &UsageStats{
+		TotalRequests:     stats.TotalRequests,
+		TotalInputTokens:  stats.TotalInputTokens,
+		TotalOutputTokens: stats.TotalOutputTokens,
+		TotalCacheTokens:  stats.TotalCacheTokens,
+		TotalTokens:       stats.TotalTokens,
+		TotalCost:         stats.TotalCost,
+		TotalActualCost:   stats.TotalActualCost,
+		AverageDurationMs: stats.AverageDurationMs,
+	}, nil
 }
 
 // GetStatsByModel 获取模型的使用统计
 func (s *UsageService) GetStatsByModel(ctx context.Context, modelName string, startTime, endTime time.Time) (*UsageStats, error) {
-	logs, _, err := s.usageRepo.ListByModelAndTimeRange(ctx, modelName, startTime, endTime)
+	stats, err := s.usageRepo.GetModelStatsAggregated(ctx, modelName, startTime, endTime)
 	if err != nil {
-		return nil, fmt.Errorf("list usage logs: %w", err)
+		return nil, fmt.Errorf("get model stats: %w", err)
 	}
 
-	return s.calculateStats(logs), nil
+	return &UsageStats{
+		TotalRequests:     stats.TotalRequests,
+		TotalInputTokens:  stats.TotalInputTokens,
+		TotalOutputTokens: stats.TotalOutputTokens,
+		TotalCacheTokens:  stats.TotalCacheTokens,
+		TotalTokens:       stats.TotalTokens,
+		TotalCost:         stats.TotalCost,
+		TotalActualCost:   stats.TotalActualCost,
+		AverageDurationMs: stats.AverageDurationMs,
+	}, nil
 }
 
 // GetDailyStats 获取每日使用统计（最近N天）
@@ -209,54 +227,12 @@ func (s *UsageService) GetDailyStats(ctx context.Context, userID int64, days int
 	endTime := time.Now()
 	startTime := endTime.AddDate(0, 0, -days)
 
-	logs, _, err := s.usageRepo.ListByUserAndTimeRange(ctx, userID, startTime, endTime)
+	stats, err := s.usageRepo.GetDailyStatsAggregated(ctx, userID, startTime, endTime)
 	if err != nil {
-		return nil, fmt.Errorf("list usage logs: %w", err)
+		return nil, fmt.Errorf("get daily stats: %w", err)
 	}
 
-	// 按日期分组统计
-	dailyStats := make(map[string]*UsageStats)
-	for _, log := range logs {
-		dateKey := log.CreatedAt.Format("2006-01-02")
-		if _, exists := dailyStats[dateKey]; !exists {
-			dailyStats[dateKey] = &UsageStats{}
-		}
-
-		stats := dailyStats[dateKey]
-		stats.TotalRequests++
-		stats.TotalInputTokens += int64(log.InputTokens)
-		stats.TotalOutputTokens += int64(log.OutputTokens)
-		stats.TotalCacheTokens += int64(log.CacheCreationTokens + log.CacheReadTokens)
-		stats.TotalTokens += int64(log.TotalTokens())
-		stats.TotalCost += log.TotalCost
-		stats.TotalActualCost += log.ActualCost
-
-		if log.DurationMs != nil {
-			stats.AverageDurationMs += float64(*log.DurationMs)
-		}
-	}
-
-	// 计算平均值并转换为数组
-	result := make([]map[string]any, 0, len(dailyStats))
-	for date, stats := range dailyStats {
-		if stats.TotalRequests > 0 {
-			stats.AverageDurationMs /= float64(stats.TotalRequests)
-		}
-
-		result = append(result, map[string]any{
-			"date":                date,
-			"total_requests":      stats.TotalRequests,
-			"total_input_tokens":  stats.TotalInputTokens,
-			"total_output_tokens": stats.TotalOutputTokens,
-			"total_cache_tokens":  stats.TotalCacheTokens,
-			"total_tokens":        stats.TotalTokens,
-			"total_cost":          stats.TotalCost,
-			"total_actual_cost":   stats.TotalActualCost,
-			"average_duration_ms": stats.AverageDurationMs,
-		})
-	}
-
-	return result, nil
+	return stats, nil
 }
 
 // calculateStats 计算统计数据