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。

scripts/cluster/run-production-acceptance.sh

@@ -667,6 +667,8 @@ mark_run_failed() {
 apply_capacity_profile() {
   local profile=$1
   local slots pool media global
+  local api_pool=48
+  local min_idle=4
   case $profile in
     P24) slots=24; pool=32; media=24; global=48 ;;
     P28) slots=28; pool=36; media=28; global=56 ;;
@@ -679,13 +681,15 @@ apply_capacity_profile() {
       "AI_GATEWAY_ASYNC_WORKER_INSTANCE_HARD_LIMIT=$slots" \
       "AI_GATEWAY_ASYNC_WORKER_HARD_LIMIT=$global" \
       "AI_GATEWAY_DATABASE_MAX_CONNS=$pool" \
+      "AI_GATEWAY_DATABASE_MIN_IDLE_CONNS=$min_idle" \
       "AI_GATEWAY_MEDIA_MATERIALIZATION_CONCURRENCY=$media" \
       "AI_GATEWAY_MEDIA_REQUEST_CONCURRENCY=$media" >/dev/null
     remote_kubectl rollout status "deployment/easyai-worker-$site" \
       -n "$namespace" --timeout=300s
     remote_kubectl set env "deployment/easyai-api-$site" -n "$namespace" \
       "AI_GATEWAY_ASYNC_WORKER_HARD_LIMIT=$global" \
-      "AI_GATEWAY_DATABASE_MAX_CONNS=$pool" >/dev/null
+      "AI_GATEWAY_DATABASE_MAX_CONNS=$api_pool" \
+      "AI_GATEWAY_DATABASE_MIN_IDLE_CONNS=$min_idle" >/dev/null
     remote_kubectl rollout status "deployment/easyai-api-$site" \
       -n "$namespace" --timeout=300s
   done
@@ -895,6 +899,7 @@ wait_for_memory_recovery() {
 
 verify_runtime_gates() {
   local expected_slots expected_global expected_pool
+  local expected_api_pool=48
   case $active_profile in
     P24) expected_slots=24; expected_pool=32; expected_global=48 ;;
     P28) expected_slots=28; expected_pool=36; expected_global=56 ;;
@@ -1055,8 +1060,8 @@ WHERE status='active'
     pool_max=$(awk '$1=="easyai_gateway_postgres_pool_max_connections" {print $2}' <<<"$metrics")
     acquired=$(awk '$1=="easyai_gateway_postgres_pool_acquired_connections" {print $2}' <<<"$metrics")
     idle=$(awk '$1=="easyai_gateway_postgres_pool_idle_connections" {print $2}' <<<"$metrics")
-    [[ ${pool_max%.*} == "$expected_pool" ]]
-    if [[ ${acquired%.*} == "$expected_pool" && ${idle%.*} == 0 ]]; then
+    [[ ${pool_max%.*} == "$expected_api_pool" ]]
+    if [[ ${acquired%.*} == "$expected_api_pool" && ${idle%.*} == 0 ]]; then
       echo "API connection pool saturated for site $site" >&2
       return 1
     fi