fix(routing): 避免路由探测耗尽数据库连接

将跨实例探测协调从持有会话级 advisory lock 改为带过期时间的数据库短租约，避免网络探测期间占用关键 PostgreSQL 连接。新增可配置的探测并发上限和真实 PostgreSQL 回归测试，确保租约生效期间连接池仍可全部获取。\n\n验证：go test ./... -count=1；go vet ./...；真实 PostgreSQL 17 集成测试；迁移安全检查。

apps/api/internal/store/execution_pools_integration_test.go

@@ -4,6 +4,9 @@ import (
 	"context"
 	"testing"
 	"time"
+
+	"github.com/easyai/easyai-ai-gateway/apps/api/internal/executionpool"
+	"github.com/jackc/pgx/v5/pgxpool"
 )
 
 func TestExecutionPoolQueriesUseTimestampCutoff(t *testing.T) {
@@ -18,3 +21,42 @@ func TestExecutionPoolQueriesUseTimestampCutoff(t *testing.T) {
 		t.Fatalf("list capacity with timestamp cutoff: %v", err)
 	}
 }
+
+func TestRouteProbeLeaseDoesNotPinDatabaseConnection(t *testing.T) {
+	db := billingV2IntegrationStore(t)
+	ctx, cancel := context.WithTimeout(context.Background(), 10*time.Second)
+	defer cancel()
+
+	if err := db.UpsertExecutionPool(ctx, executionpool.ExecutionPool{ID: "probe-pool", State: executionpool.PoolActive}); err != nil {
+		t.Fatalf("upsert execution pool: %v", err)
+	}
+	token, claimed, err := db.TryClaimRouteProbe(ctx, "probe-pool", "route-profile", 15*time.Second)
+	if err != nil {
+		t.Fatalf("claim route probe: %v", err)
+	}
+	if !claimed || token == "" {
+		t.Fatal("route probe was not claimed")
+	}
+
+	connections := make([]*pgxpool.Conn, 0, db.Pool().Stat().MaxConns())
+	defer func() {
+		for _, connection := range connections {
+			connection.Release()
+		}
+	}()
+	for range db.Pool().Stat().MaxConns() {
+		connection, err := db.Pool().Acquire(ctx)
+		if err != nil {
+			t.Fatalf("acquire all pool connections while lease is active: %v", err)
+		}
+		connections = append(connections, connection)
+	}
+	for _, connection := range connections {
+		connection.Release()
+	}
+	connections = connections[:0]
+
+	if err := db.ReleaseRouteProbe(ctx, "probe-pool", "route-profile", token); err != nil {
+		t.Fatalf("release route probe: %v", err)
+	}
+}