Issue with Nuxt 3.1.0 and Web Worker / Vuetify usage

This is a minimal reproduction of an issue concerning Nuxt v3.1.0 and the usage of Web Workers and Vuetify.

This repo loads Vuetify, and has a single v-btn that will load a Web Worker to do some calculations in a different thread, and then post the result back to the main thread where it is displayed.

This works OK when using Nuxt 3.0.0. But if you upgrade to Nuxt 3.1.0 or higher, it breaks. The Vuetify styling disappears (the CSS is nowhere to be seen) and the Web Worker script goes mental.

Note that the error only occurs when you build for production. The dev server always works without a hitch.

Reproduction

Install the dependencies:

# yarn
yarn install

# npm
npm install

# pnpm
pnpm install

Test on v.3.0.0

Build the application for production:

npm run build

Locally preview production build:

npm run preview

You should now see a page with a single button, 'Call Worker'. Press it and the button thinks for a bit while the worker thread does the calculations, then reports back with a piece of text under the button.

You can also see log messages from the worker in the console.

Test on v 3.1.0

Edit the package.json and change the "nuxt" dependency to "3.1.0", then install the new version.

# yarn
yarn install

# npm
npm install

# pnpm
pnpm install

Build the application for production:

npm run build

Locally preview production build:

npm run preview

You should now not see the button anymore. Open the console and notice that the web worker is being called with the value '0' over and over again.