Example from README does not work

I'm trying to decide if this is just a documentation issue or if there's something else going on. Starting a brand new Astro project via npm create astro@latest and then attempting to add this dependency, throws an error:

Cannot find module '/home/jim/Sites/ostk-header/api/index.js' imported from /home/jim/Sites/ostk-header/node_modules/@matthewp/astro-fastify/lib/index.js
Error [ERR_MODULE_NOT_FOUND]: Cannot find module '/home/jim/Sites/ostk-header/api/index.js' imported from /home/jim/Sites/ostk-header/node_modules/@matthewp/astro-fastify/l
ib/index.js
    at new NodeError (node:internal/errors:393:5)

Well that's simple enough, right? We named the file api/index.ts. So, let's change that in the config:

import fastify from '@matthewp/astro-fastify';

/** @type {import('astro').AstroUserConfig} */
export default {
  output: 'server',
  adapter: fastify({
    entry: new URL('./api/index.ts', import.meta.url)
  })
};

But that'll throw:

Unknown file extension ".ts" for /home/jim/Sites/ostk-header/api/index.ts
TypeError [ERR_UNKNOWN_FILE_EXTENSION]: Unknown file extension ".ts" for /home/jim/Sites/ostk-header/api/index.ts
    at new NodeError (node:internal/errors:393:5)
    at Object.getFileProtocolModuleFormat [as file:] (node:internal/modules/esm/get_format:80:11)
    at defaultGetFormat (node:internal/modules/esm/get_format:122:38)

As we're trying to us ESM imports, not Typescript. So let's try naming the file index.js. From the presence of a type definition, it looks like you really did mean for it to be Typescript though. Regardless, that doesn't work.

Finally, let's name the file .mjs and change the reference to ./api/index.mjs. THAT seems to work. I don't think that was your intention though. I really do think you wanted to use Typescript so... what might I be missing here?

matthewp / astro-fastify

Example from README does not work #1