The way I see it, there are 3 main ways to use Vue with Laravel:
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Use Inertia with Vue. Probably the most popular these days. Requires full commitment to Vue for your entire front-end. Series here: https://laracasts.com/series/build-modern-laravel-apps-using-inertia-js
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Drop in Vue components into your blade files. Was popular in the past. Example with compiling Vue Single FIle Components with Vite: https://laracasts.com/series/andres-larabits/episodes/31
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Have a separate repo for your frontend and backend. Frontend in Vue/Nuxt, backend is an API in Laravel: Example: https://laracasts.com/series/nuxtjs-crash-course