Can a TestNG cross-browser test be executed with Cucumber runner?

Question

I am working with Selenium Webdriver with Cucumber. My tests work as expected with that combination. In order to achieve cross-browser testing, I added TestNG framework. To verify that my cross-browser test was working good, I ran it with TestNG alone, without Cucumber. It ran perfectly in both Chrome and Firefox browsers.

public class WebTest {


  WebDriver driver = null;
  BasePageWeb basePage;
  public String browser;


  @Parameters({ "Browser" })
  public WebTest(String browser) {
    this.browser = browser;
  }

  
  @BeforeClass
  public void navigateToUrl() {
    switch (browser) {

      case "CHROME":
        WebDriverManager.chromedriver().setup();
        driver = new ChromeDriver();
        break;

      case "FF":
        WebDriverManager.firefoxdriver().setup();
        driver = new FirefoxDriver();
        break;

      default:
        driver = null;
        break;
    }
    driver.get("https://demosite.executeautomation.com/Login.html");

  }

  @Test
  public void loginToWebApp() {

    basePage = new BasePageWeb(driver);
    basePage.enterUsername("admin")
            .enterPassword("admin")
            .clickLoginButton();

    driver.quit();
  }

}

The testng.xml file:

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE suite SYSTEM "http://testng.org/testng-1.0.dtd">

<suite name="Suite" parallel="tests" thread-count="5">

    <test name="Chrome Test">
        <parameter name="Browser" value="CHROME"/>
        <classes>
            <class name="tests.web.WebTest"/>
        </classes>
    </test>
    <test name="Firefox Test">
        <parameter name="Browser" value="FF"/>
        <classes>
            <class name="tests.web.WebTest"/>
        </classes>
    </test>
</suite>

I needed to integrate the TestNG test with my Cucumber set-up so that I can run the whole test with Cucumber. To do this, I added cucumber-testng dependency to POM and created a Cucumber runner extending the AbstractCucumberTestNG class. I specified the location of my feature file and step definition. The step definition is mapped to the TestNG test.

Cucumber runner:

@CucumberOptions(
                plugin = {"pretty", "html:target/surefire-reports/cucumber",
                        "json:target/surefire-reports/cucumberOriginal.json"},
                glue = {"stepdefinitions"},
                tags = "@web-1",
                features = {"src/test/resources/features/web.feature"})
          
   

 public class RunCucumberNGTest extends AbstractTestNGCucumberTests {
    }

Step definition:

public class WebAppStepDefinitions {
      private final WebTest webTest = new WebTest("CHROME"); //create an object of the class holding the testng test. If I change the argument to FF, the test will run only on Firefox
      static boolean prevScenarioFailed = false;
    
    
      @Before
      public void setUp() {
        if (prevScenarioFailed) {
          throw new IllegalStateException("Previous scenario failed!");
        }
    
      }
    
      @After()
      public void stopExecutionAfterFailure(Scenario scenario) throws Exception {
        prevScenarioFailed = scenario.isFailed();
      }
    
      @Given("^I have navigated to the web url \"([^\"]*)\"$")
      public void navigateToUrl(String url) {  test
        webTest.navigateToUrl(url); //calling the first method holding the testng
      }
    
    
      @When("^I log into my web account with valid credentials as specicified in (.*) and (.*)$")
      public void logintoWebApp(String username, String password) {
        webTest.loginToWebApp(username, password); //calling the second method holding the testng
      }
    }

On running the class, the test got executed only in one browser (Chrome). Somehow, Firefox got lost in the build-up. I suspect that I am calling the parameterised TestNG method wrongly from another class. How do I do the call successfully?