By default Hugo doesn't serve .mjs files with the correct content type. In fact it wasn't until recently that hugo could serve more than one file extension per mime-type. It looks like with v0.43 this has been fixed.
About Me: Paul Kinlan
I lead the Chrome Developer Relations team at Google.
We want people to have the best experience possible on the web without having to install a native app or produce content in a walled garden.
Our team tries to make it easier for developers to build on the web by supporting every Chrome release, creating great content to support developers on web.dev, contributing to MDN, helping to improve browser compatibility, and some of the best developer tools like Lighthouse, Workbox, Squoosh to name just a few.