same laravel_session value, but not the same value

i’m using laravel 12 and try to use middleware to check the user is login or not.

I set the session value in api Controller, but, when I call this value in middleware, it will be null.
and my log only show the token in session.
how to get session value correctly?

my laravel_session in header and session value in database:
laravel_session=fca6d3xPRfTdlHBSTJWBd0KvaieSdKPbcGkFBZxa

a:3:{s:6:"_token";s:40:"0hYLgh1hHAZNW2Ar8E6MDBP5zKJXlLynSjt4dgTp";s:4:"user";s:5:"admin";s:6:"_flash";a:2:{s:3:"old";a:0:{}s:3:"new";a:0:{}}}

i’m use the session function to set global session value.
i’m sure that name is not null.

        // loginVerify
        $validate = $request->authenticate();

        if ($validate) {
            $post = $request->post()['body'];
    
            $acct = User::where([['email', '=', $post['acct']],['password', '=', $post['ps']]])->first();
            session(['user' => $acct['name']]);
            return $acct;
        }

log not show user value in my session

my session value: {"_token":"T9EtbOAiUwUYc9s1l1gC4TrdSkTj8nT9SDFbqTIA"}

    // middleware managePage
    public function handle(Request $request, Closure $next): Response
    {
        Log::debug ('my session value: ' . json_encode(session()->all()));
        dd($request->header('Cookie'));
        if (empty(session('user'))) {
            return redirect('/managerLogin');
        }
        return $next($request);
    }

here is my middleware setting:

        $middleware->prependToGroup('manageSetting', [
            IlluminateSessionMiddlewareStartSession::class,
        ]);
        $middleware->appendToGroup('managePage', [
            ManagerPage::class,
        ]);

and this is my route setting:

// web route
Route::middleware(['manageSetting', 'managePage'])->group(function () {
    Route::get('/homeManage', function () {
        return Inertia::render('manage/homeManage');
    });
    Route::get('/groupManage', function () {
        return Inertia::render('manage/groupManage');
    });
});
Route::middleware(['manageSetting'])->group(function() {

    Route::get('/managerLogin', function () {
        return Inertia::render('manage/login');
    })->name('managerlogin');
});

//api route
Route::middleware(['manageSetting'])->group(function () {
    Route::post('/updateGroup', [GroupController::class, 'update']);
    Route::post('/updateHome', [KeyVisualController::class, 'update']);
    Route::post('/loginVerify', [UserController::class, 'login']);
});