---

мне кажется ты уходишь от нашей структуры, напомню тебе еще раз ее
допиши AuthClient

.
├── AuthClient.java
├── AuthConfiguration.java
├── AuthExeption.java
├── AuthService.java
├── CertificateLoader.java
└── CookieHolder.java

public class AuthClient {
  public String authorize() {
    KeyStore keyStore = CertificateLoader.load();
    //TODO

    Response response = (Response) RestAssured
            .given()
            //.config()
            .get(AuthConfiguration.AUTH_URL);

    String cookie = response.headers().toString();
    if (cookie == null) {
        throw new AuthExeption("Cookie is null", null);
    }
    return cookie;
  }

}

public class AuthService {
  private final AuthClient authClient = new AuthClient();
  private final CookieHolder holder = new CookieHolder();

  public String getCookie() {
    if (holder.isEmpty()) {
      synchronized (this) {
        if (holder.isEmpty()) {
          holder.set(authClient.authorize());
        }
      }
    }
    return holder.get();
  }

  public void refresh() {
    holder.set(authClient.authorize());
  }

}

public class CertificateLoader {
  private CertificateLoader () {}

  public static KeyStore load() {
    try(InputStream is = Files.newInputStream(
        Paths.get(AuthConfiguration.CERTIFICATE_PATH))) {
      KeyStore keyStore = KeyStore.getInstance("PKS12");
        keyStore.load(is, AuthConfiguration.CERTIFICATE_PASSWORD.toCharArray());
        return keyStore;
    } catch (Exception e) {
        throw new AuthExeption("Не могу загрузить сертификат, ошибка: ", e);
    }
  }
}

public class CookieHolder {
  private volatile String cookie;

  public String get() {
      return cookie;
  }

  public void set(String cookie) {
      this.cookie = cookie;
  }

  public boolean isEmpty() {
      return cookie == null || cookie.isBlank();
  }

  public void clear() {
      cookie = null;
  }
}