Lambda: Can't use typescript module files

[dj-rabel]

Describe the bug

We've tried to compile ESM output (.mjs) files from .mts (TypeScript Module) files via CDK "NodejsFunction". We don't want to change everything in our project to be JavaScript module code. So the only option is to use .mjs, or in our case, .mts files.
But someone thought it is a good idea to prohibit any other file extensions than .jsx?, .tsx? or .mts. So we're constantly getting an error that .mts is not valid. (which it is and should be allowed)

aws-cdk/packages/aws-cdk-lib/aws-lambda-nodejs/lib/function.ts

Line 165 in 28914bd

if (!/\.(jsx?|tsx?|mjs)$/.test(entry)) {

As soon as I remove the referenced line from the functions.js it compiles and deploys fine ...

Expected Behavior

At least .mts should be allowed as well if there is .ts and .mjs allowed.

https://www.typescriptlang.org/docs/handbook/esm-node.html#new-file-extensions

Maybe it is a good idea to allow .cjs and .cts as well these days 😅

Current Behavior

Error "Only JavaScript or TypeScript entry files are supported." is thrown even for perfectly valid TypeScript files. Probably even for perfectly valid JavaScript files with the ending .cjs.

Reproduction Steps

Stack code to create lambda using mts file and ESM format.

import * as lambda from "aws-cdk-lib/aws-lambda-nodejs";
import { Runtime as LambdaRuntime } from "aws-cdk-lib/aws-lambda";

new lambda.NodejsFunction(this, 'DummyLambda', {
    entry: path.join('src', `DummyLambda.mts`),
    runtime: LambdaRuntime.NODEJS_16_X,
    bundling: {
        charset: lambda.Charset.UTF8,
        format: lambda.OutputFormat.ESM,
        target: "node16.15",
        @see https://github.com/evanw/esbuild/issues/584#issuecomment-740170568
        esbuildArgs: {
            "--main-fields": "module,main",
        },
    },
});

Contents of specified DummyLambda.mts can be any typescript code. Doenst matter for generating the error. The file isn't even required to exist.

Possible Solution

Regarding to https://www.typescriptlang.org/docs/handbook/esm-node.html#new-file-extensions at least .mts should be allowed. I would suggest to allow .cjs and .cts as well.

Additional Information/Context

No response

CDK CLI Version

2.37.1

Framework Version

No response

Node.js Version

All

OS

All

Language

Typescript

Language Version

All

Other information

No response

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