logout after session expire?

You can handle that manually, in your Exceptions\Handler.php class add this in the render method:

if ($exception instanceof TokenMismatchException) {
     return redirect('login')->with('message', 'An error message.');
}

now im using laravel 9 and search for solution to this issue i found that the problem is VerifyCsrfToken middleware called before Authenticate middleware and if we just reorder the calling of this two middleware the issue will fixed so i just add this code to app/Http/Keernel.php

protected $middlewarePriority = [
    \App\Http\Middleware\Authenticate::class,
    \App\Http\Middleware\VerifyCsrfToken::class,
];