You’re using absolute links to your assets, so as you can see by the error you’re getting it’s trying to access them at the root of the domain, https://CLIENTID.ext-twitch.tv, but Twitch doesn’t serve your files from the root, it serves it from a path that looks like https://CLIENTID.ext-twitch.tv/CLIENTID/VERSION/HASH/.
So you need to refer to the documentation for your build process and fix its config so that it builds with relative links, such as ./some-file.js, or some-file.js, not /some-file.js.
I’m not a Vite user myself, but I believe the way you would change it is by using the base option, https://vitejs.dev/config/shared-options.html#base, as it defaults to / so setting it to an empty string, '', should work.