sorry for the late replay, to handle authentication I assume you are going to use Laravel Breeze, with interejs it gets Handel automatically you don't have to worry about it, in your laravel code you get access to the auth variable and Middleware, and in you vue/react file you also get access to auth, this auth is updated with every request and can be found and changes in
HandleInertiaRequests.php file also known as Shared data. i suggest you take a look at this link as they did explain it better than me
link