Serverless to CDK bridge with HttpApi extension

serverless.ts

import type { AWS } from '@serverless/typescript';
import { App, Stack, Fn } from 'aws-cdk-lib';
// import { CfnApiMapping } from 'aws-cdk-lib/aws-apigatewayv2'
import { Certificate } from 'aws-cdk-lib/aws-certificatemanager'
import { ApiMapping, DomainName, HttpApi, HttpStage } from '@aws-cdk/aws-apigatewayv2-alpha';

const app = new App();
class MyStack extends Stack {
  constructor(scope, id) {
    super(scope, id);

    // new CfnApiMapping(this, 'MyMappingl1', {
    //   apiId: Fn.ref('HttpApi'),
    //   domainName: 'toto',
    //   apiMappingKey: 'tata',
    //   stage: 'mystage',
    // })

    const serverlessProvisionnedHttpApi = HttpApi.fromHttpApiAttributes(this, 'MyApi', {
      httpApiId: Fn.ref('HttpApi'),
    })
    // const newHttApi = new HttpApi(this, 'NewAPI');
    const dn = new DomainName(this, 'DN', {
      domainName: 'exemple.com',
      certificate: Certificate.fromCertificateArn(this, 'cert', 'arn:aws:acm:us-east-1:111111111111:certificate'),
    });

    new ApiMapping(this, 'MyMappingL2', {
      api: serverlessProvisionnedHttpApi,
      domainName: dn,
      stage: HttpStage.fromHttpStageAttributes(this, 'defaultStage', {
        api: serverlessProvisionnedHttpApi,
        stageName: '$default',
      })
    })

    // new HttpApi(this, 'HttpProxyProdApi', {
    //   // https://${dn.domainName}/foo goes to prodApi $default stage
    //   defaultDomainMapping: {
    //     domainName: dn,
    //     mappingKey: 'foo',
    //   },
    // });
  }
}
const myStack = new MyStack(app, 'MyStack');

import hello from '@functions/hello';

const serverlessConfiguration: AWS = {
  service: 'tmp',
  frameworkVersion: '2',
  plugins: ['serverless-esbuild', 'serverless-lift'],
  provider: {
    name: 'aws',
    runtime: 'nodejs14.x',
    region: 'eu-west-1',
    apiGateway: {
      minimumCompressionSize: 1024,
      shouldStartNameWithService: true,
    },
    environment: {
      AWS_NODEJS_CONNECTION_REUSE_ENABLED: '1',
      NODE_OPTIONS: '--enable-source-maps --stack-trace-limit=1000',
    },
    lambdaHashingVersion: '20201221',
  },
  // import the function via paths
  functions: { hello },
  package: { individually: true },
  resources: app.synth().getStackByName(myStack.stackName).template,
  custom: {
    esbuild: {
      bundle: true,
      minify: false,
      sourcemap: true,
      exclude: ['aws-sdk'],
      target: 'node14',
      define: { 'require.resolve': undefined },
      platform: 'node',
      concurrency: 10,
    },
  },
};

module.exports = serverlessConfiguration;