InertiaJS redirecting to another components does not render

Question

I'm using Laravel and InertiaJS and Vue 3 to create an application. I have a simple login page (username and password only), When the user logs in, I want to redirect him to the homepage. I have two Vue components - Login and Home.

This the function I'm using in LoginController:

public function store() {
    $attributes = request() -> validate([
        'username' => 'required|min:4',
        'password' => 'required|min:8',
    ]);

    if(auth()->attempt($attributes)) // <-- returns true.
        return Route::redirect('/home');
}

I have this Route in my web.php:

Route::get('/home', function() {
    return Inertia::render('Home');
})

When the user tries to login, it logs in correctly, but does not refresh. after manual refresh the user does gets to the homepage, but I want the redirection to be automatic.

The post request to store is through axios, I have this on my Login.Vue:

login() {
    axios.post('login', {
        username: this.username,
        password: this.password
    })
}

I read the docs, and saw few questions here, but it didn't work for me for some reason.