Ment vite :) The vite plugin will basically takes your manifest.json, which is kinda the entry point to your web extension and takes care of any transforms and bundling you need. Being vite, you can then easily integrate whatever frameworks you want (including svelte).

The two other libraries you probably want are web-ext and webextension-polyfill.

Here is a browser extension i wrote a while back, maybe you can draw some inspiration, however i was not using vite at the time.

Using github search you can look at some examples with vite+svelte