Track the last activity in laravel

In laravel auth middleware i create session variable and store the the last entering time like

class Authenticate extends Middleware
{
    public function handle($request, Closure $next, ...$guards)
{
    if (auth()->check()) {
        session()->put('activity_time', now()->toDateTimeString());
    }
    return parent::handle($request, $next, ...$guards);
}


protected function redirectTo(Request $request): ?string
{
   
    if ($request->expectsJson()) {
        
        return null;
    }

    return route('root');
}

}

In route

Route::get('/', [AuthController::class, 'index'])->middleware('guest')->name('root');
Route::middleware(['auth'])->group(function () {
    Route::resource('home', HomeController::class);
    Route::resource('student', StudentController::class);
});

in above route we do any operations in side the auth group that time session last active is updated?

and i create another middelware for check the time diffrence like

class CheckLastActivityTime
{
    public function handle(Request $request, Closure $next)
{
    $lastActivity = session()->get('activity_time');
    // var_dump($lastActivity); die();
    if ($lastActivity) {
        $lastActivity = Carbon::parse($lastActivity);

        if (Carbon::now()->diffInMinutes($lastActivity) > 5) {
            auth()->logout();
            session()->invalidate();
            session()->regenerateToken();

            return redirect('root')->with('error', 'Your session has expired. Please log in again.');
        }
    }

    return $next($request);
}
}

And this middleware register in kernel

protected $middleware = [
    // ...
    AppHttpMiddlewareCheckLastActivityTime::class,
];

and i dd the $lastActivity in the middleware it’s show null, how we can track the time and logout the user?