If you want to use Vue with Laravel, it's better to use Interia.js, so you don't have to worry about routing with vue, and using Laravel only as a backend and all the pain that comes with managing/securing tokens, and you're in luck because Laracasts has the best course I've seen so far:
Quick note: This course uses Laravel 8 (Webpack), the current version is Laravel 9 which uses Vite by default now, so you need to do a bit of changes in order to get it to work, once done configuring everything is the same, here are the docs: