aws lambda - ES6 module error : module is not defined in ES module scope

Based on these resources :

https://aws.amazon.com/about-aws/whats-new/2022/01/aws-lambda-es-modules-top-level-await-node-js-14/ https://aws.amazon.com/blogs/compute/using-node-js-es-modules-and-top-level-await-in-aws-lambda/

it is clear that aws nodejs 14.x now supports ES6 module.

However, when I to run a nodejs app with ES6 module, I get this error

undefined   ERROR   Uncaught Exception  
{
    "errorType": "ReferenceError",
    "errorMessage": "module is not defined in ES module scope\nThis file is being treated as an ES module because it has a '.js' file extension and '/var/task/package.json' contains \"type\": \"module\". To treat it as a CommonJS script, rename it to use the '.cjs' file extension.",
    "stack": [
        "ReferenceError: module is not defined in ES module scope",
        "This file is being treated as an ES module because it has a '.js' file extension and '/var/task/package.json' contains \"type\": \"module\". To treat it as a CommonJS script, rename it to use the '.cjs' file extension.",
        "    at file:///var/task/index.js:20:1",
        "    at ModuleJob.run (internal/modules/esm/module_job.js:183:25)",
        "    at process.runNextTicks [as _tickCallback] (internal/process/task_queues.js:60:5)",
        "    at /var/runtime/deasync.js:23:15",
        "    at _tryAwaitImport (/var/runtime/UserFunction.js:74:12)",
        "    at _tryRequire (/var/runtime/UserFunction.js:162:21)",
        "    at _loadUserApp (/var/runtime/UserFunction.js:197:12)",
        "    at Object.module.exports.load (/var/runtime/UserFunction.js:242:17)",
        "    at Object.<anonymous> (/var/runtime/index.js:43:30)",
        "    at Module._compile (internal/modules/cjs/loader.js:1085:14)"
    ]
}

I have already added "type": "module" in package.json

package.json

{
  "name": "autoprocess",
  "version": "1.0.0",
  "description": "",
  "main": "index.js",
  "type": "module",
  "scripts": {
    
  },
  "author": "",
  "license": "ISC",
  "dependencies": {
    "@aws-sdk/client-sqs": "^3.41.0",
    "aws-sdk": "^2.1030.0",
    "check-if-word": "^1.2.1",
    "express": "^4.17.1",
    "franc": "^6.0.0",
    "is-html": "^3.0.0",
    "nodemon": "^2.0.15"
  }
}

index.json

'use strict';

import StringMessage from  './StringMessage.js';

module.exports.handler = async (event) => {
   var data = JSON.parse(event.body);
    //other code goes here

   let response = {
      statusCode: 200,
      headers: {          
      },
      body: ""
  };
  console.log("response: " + JSON.stringify(response))
  return response;
};

I have also tried replacing "module.exports.handler" with "exports.handler ". this does not work either. error message shows "exports is not defined in ES module scope"

What am I doing wrong?

additional info: I am uploading the function code via zip file