Cookie auth api

How to send requests from the server to the API of another service if authorization is through cookies?

My goal is to log in to the API of a third-party service through my server, but every time I get a message that the session_expired

public function __construct(string $login, string $password)
    {
        $this->client = Http::baseUrl('another_api_link');
        $this->login = $login;
        $this->password = $password;

        if (!Cache::has($login)) {
            $requestCookies = $this->auth($login, $password)->cookies();
            Cache::put($login, $requestCookies, 3000);
        }
    }

public function auth($login, $password): Response
    {
        return $this
            ->client
            ->asForm()
            ->post(
                '/',
                [
                    'login' => $login,
                    'password' => $password,
                ]
            );
    }

public function yesterdayBookings()
    {
        $yesterday = date('Y-m-d', strtotime('-1 day'));

        return $this
            ->client
            ->withHeaders([
                'X-Requested-With' => 'XMLHttpRequest',
            ])
            ->withOptions(['cookies' => Cache::get($this->login)])
            ->post(
                '/planning/bookings',
                [
                    'dfrom' => $yesterday,
                    'dto' => $yesterday,
                    'daily' => 1,
                ]
            );
    }

Next, I try to do the following via Tinker:

$class = new Namespace\MyClass($login, $password);

$response = $class->yesterdayBookings();

$response->body()

Output:

session_expired