For whom who might run into the same issue, here is one example how to explicitly declare the `provider`:

// Create an EKS cluster with the default configuration.
const cluster = new eks.Cluster("my-cluster");

const service = new k8s.core.v1.Service(`${appName}-svc`, {
    metadata: { labels: appLabels },
    spec: {
        type: "LoadBalancer",
        ports: [{ port: 80, targetPort: "http" }],
        selector: appLabels,
    },
}, { provider: cluster.provider });

pay attention to the resource options

{ provider: cluster.provider }