perf(postgres): 分离 API 池并降低连接预热

生产同构千并发请求在干净队列上复现 API Pool 31/32、idle=1 且 canceled acquire 持续增长，Worker Pool 仅使用少量连接，确认瓶颈位于 API 数据库连接预算而非 Worker 执行槽。

新增可配置的 AI_GATEWAY_DATABASE_MIN_IDLE_CONNS，生产仅预热 4 条连接；API Pool 独立固定为 48，Worker Pool 继续跟随 P24/P28/P32 的 32/36/40 档位。发布工具、Kubernetes 清单、验收门禁和文档同步更新。

验证：Go 全量测试、gofmt、bash -n、ShellCheck、kubectl kustomize 和 git diff --check 通过。

apps/api/internal/config/config.go

@@ -59,6 +59,7 @@ type Config struct {
 	BillingEngineMode                             string
 	ProcessRole                                   string
 	DatabaseMaxConns                              int
+	DatabaseMinIdleConns                          int
 	DatabaseIdleInTransactionTimeoutSeconds       int
 	DatabaseLockTimeoutSeconds                    int
 	MediaRequestConcurrency                       int
@@ -122,6 +123,7 @@ func Load() Config {
 		BillingEngineMode:               strings.ToLower(env("BILLING_ENGINE_MODE", "observe")),
 		ProcessRole:                     strings.ToLower(strings.TrimSpace(env("AI_GATEWAY_PROCESS_ROLE", "all"))),
 		DatabaseMaxConns:                envInt("AI_GATEWAY_DATABASE_MAX_CONNS", 0),
+		DatabaseMinIdleConns:            envOptionalIntValidated("AI_GATEWAY_DATABASE_MIN_IDLE_CONNS", 0),
 
 		DatabaseIdleInTransactionTimeoutSeconds: envOptionalIntValidated(
 			"AI_GATEWAY_DATABASE_IDLE_IN_TRANSACTION_TIMEOUT_SECONDS",
@@ -147,6 +149,10 @@ func (c Config) Validate() error {
 	if c.DatabaseMaxConns < 0 || c.DatabaseMaxConns > 1000 {
 		return errors.New("AI_GATEWAY_DATABASE_MAX_CONNS must be between 1 and 1000 when configured")
 	}
+	if c.DatabaseMinIdleConns < 0 || c.DatabaseMinIdleConns > 1000 ||
+		(c.DatabaseMaxConns > 0 && c.DatabaseMinIdleConns > c.DatabaseMaxConns) {
+		return errors.New("AI_GATEWAY_DATABASE_MIN_IDLE_CONNS must be between 0 and AI_GATEWAY_DATABASE_MAX_CONNS")
+	}
 	if c.DatabaseIdleInTransactionTimeoutSeconds < 0 || c.DatabaseIdleInTransactionTimeoutSeconds > 3600 {
 		return errors.New("AI_GATEWAY_DATABASE_IDLE_IN_TRANSACTION_TIMEOUT_SECONDS must be between 0 and 3600")
 	}