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/infrastructure/db_pool_test.go

@@ -0,0 +1,50 @@
+package infrastructure
+
+import (
+	"database/sql"
+	"testing"
+	"time"
+
+	"github.com/Wei-Shaw/sub2api/internal/config"
+	"github.com/stretchr/testify/require"
+
+	_ "github.com/lib/pq"
+)
+
+func TestBuildDBPoolSettings(t *testing.T) {
+	cfg := &config.Config{
+		Database: config.DatabaseConfig{
+			MaxOpenConns:           50,
+			MaxIdleConns:           10,
+			ConnMaxLifetimeMinutes: 30,
+			ConnMaxIdleTimeMinutes: 5,
+		},
+	}
+
+	settings := buildDBPoolSettings(cfg)
+	require.Equal(t, 50, settings.MaxOpenConns)
+	require.Equal(t, 10, settings.MaxIdleConns)
+	require.Equal(t, 30*time.Minute, settings.ConnMaxLifetime)
+	require.Equal(t, 5*time.Minute, settings.ConnMaxIdleTime)
+}
+
+func TestApplyDBPoolSettings(t *testing.T) {
+	cfg := &config.Config{
+		Database: config.DatabaseConfig{
+			MaxOpenConns:           40,
+			MaxIdleConns:           8,
+			ConnMaxLifetimeMinutes: 15,
+			ConnMaxIdleTimeMinutes: 3,
+		},
+	}
+
+	db, err := sql.Open("postgres", "host=127.0.0.1 port=5432 user=postgres sslmode=disable")
+	require.NoError(t, err)
+	t.Cleanup(func() {
+		_ = db.Close()
+	})
+
+	applyDBPoolSettings(db, cfg)
+	stats := db.Stats()
+	require.Equal(t, 40, stats.MaxOpenConnections)
+}