Failing to create DataDog Lambda layer for Next.js website deployed through SST v2 framework

I am deploying a Next.js website to AWS via the SST v2 framework. I want to monitor it via DataDog. Below are the contents of my sst.config.ts file. I am not getting any errors during the deployment but nothing happens either. The website gets deployed,but the DataDog Lambda layer does not get created and attached to the Lambda function.

import { SSTConfig } from "sst";
import { NextjsSite } from "sst/constructs";
import { DatadogLambda } from "datadog-cdk-constructs-v2";

export default {
  config(_input) {
    return {
      name: "sst-test",
      region: "us-east-1",
    };
  },
  stacks(app) {
    app.stack(function Site({ stack }) {
      const datadog = new DatadogLambda(stack, "DatadogLambda", {
        nodeLayerVersion: 121,
        extensionLayerVersion: 77,
        site: "datadoghq.com",
        apiKeySecretArn: "<DATADOG_API_KEY_SECRET_ARN>" 
      });
      const site = new NextjsSite(stack, "site",{
        runtime: "nodejs20.x",
      });
      datadog.addLambdaFunctions(stack.getAllFunctions());
      stack.addOutputs({
        SiteUrl: site.url,
      });
    });
  },
} satisfies SSTConfig;

After checking the logs, it seems SST ignores the DataDog section of the config.