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。

deploy/kubernetes/production/application.yaml

@@ -53,7 +53,9 @@ spec:
             - name: AI_GATEWAY_ASYNC_QUEUE_WORKER_ENABLED
               value: "false"
             - name: AI_GATEWAY_DATABASE_MAX_CONNS
-              value: "32"
+              value: "48"
+            - name: AI_GATEWAY_DATABASE_MIN_IDLE_CONNS
+              value: "4"
             - name: AI_GATEWAY_MEDIA_REQUEST_CONCURRENCY
               value: "16"
             - name: AI_GATEWAY_MEDIA_MATERIALIZATION_CONCURRENCY
@@ -182,7 +184,9 @@ spec:
             - name: AI_GATEWAY_ASYNC_QUEUE_WORKER_ENABLED
               value: "false"
             - name: AI_GATEWAY_DATABASE_MAX_CONNS
-              value: "32"
+              value: "48"
+            - name: AI_GATEWAY_DATABASE_MIN_IDLE_CONNS
+              value: "4"
             - name: AI_GATEWAY_MEDIA_REQUEST_CONCURRENCY
               value: "16"
             - name: AI_GATEWAY_MEDIA_MATERIALIZATION_CONCURRENCY
@@ -312,6 +316,8 @@ spec:
               value: "true"
             - name: AI_GATEWAY_DATABASE_MAX_CONNS
               value: "32"
+            - name: AI_GATEWAY_DATABASE_MIN_IDLE_CONNS
+              value: "4"
             - name: AI_GATEWAY_ASYNC_WORKER_INSTANCE_HARD_LIMIT
               value: "24"
             - name: AI_GATEWAY_MEDIA_MATERIALIZATION_CONCURRENCY
@@ -443,6 +449,8 @@ spec:
               value: "true"
             - name: AI_GATEWAY_DATABASE_MAX_CONNS
               value: "32"
+            - name: AI_GATEWAY_DATABASE_MIN_IDLE_CONNS
+              value: "4"
             - name: AI_GATEWAY_ASYNC_WORKER_INSTANCE_HARD_LIMIT
               value: "24"
             - name: AI_GATEWAY_MEDIA_MATERIALIZATION_CONCURRENCY