How to push another page in iOS programmatically?

I am working with one project on Xcode with SnapKit and without storyboard.
I didn’t touch AppDelegate.
I have this code on SceneDelegate.

import UIKit

class SceneDelegate: UIResponder, UIWindowSceneDelegate {
    var window: UIWindow?

    func scene(_ scene: UIScene, willConnectTo session: UISceneSession, options connectionOptions: UIScene.ConnectionOptions) {
        guard let windowScene = (scene as? UIWindowScene) else { return }
        window = UIWindow(windowScene: windowScene)
        window?.makeKeyAndVisible()
        window?.rootViewController = TabBarController()
    }
}

Project’s hierarchy like that:

• HomePage(Group)

1. TabBarController
2. ViewController
3. HomeCollectionViewCell

• ShopPage(Group)
  …

• MessagePage(Group)
  …

• ProfilePage(Group)

1. ProfileViewController
2. SettingsViewController

I want to open SettingsViewController when settingsButton(on ProfileViewController) tapped.

This is my code in the TabBarController:

import UIKit

class TabBarController: UITabBarController {
    override func viewDidLoad() {
        super.viewDidLoad()
        self.setupTabs()
        selectedIndex = 3
        tabBar.backgroundColor = .systemBackground
        tabBar.tintColor = UIColor(red: 0, green: 155/255, blue: 247/255, alpha: 1)
    }
    
    //MARK: - Tab Setup
    private func setupTabs(){
        let home = self.createNav(title: "Home", image: UIImage(systemName: "house"), vc: ViewController())
        let shop = self.createNav(title: "Shop", image: UIImage(systemName: "bag"), vc: ShopViewController())
        let message = self.createNav(title: "Message", image: UIImage(systemName: "ellipsis.message"), vc: MessageViewController())
        let profile = self.createNav(title: "Profile", image: UIImage(systemName: "person"), vc: ProfileViewController())
        self.setViewControllers([home, shop, message, profile], animated: true)
    }
    
    private func createNav(title: String, image: UIImage?, vc: UIViewController) -> UINavigationController{
        let nav = UINavigationController(rootViewController: vc)
        nav.tabBarItem.title = title
        nav.tabBarItem.image = image
        return nav
    }
}

This is my code in the ProfileViewController:

class ProfileViewController: UIViewController {
    private lazy var settingButton: UIButton = {
        let button = UIButton()
        button.setImage(UIImage(systemName: "gearshape"), for: .normal)
        button.addTarget(self, action: #selector(openSettings), for: .touchUpInside)
        return button
    }()

    override func viewDidLoad() {
        super.viewDidLoad()
        view.backgroundColor = UIColor(red: 250/255, green: 250/255, blue: 250/255, alpha: 1)
        setupUI()
    }
    
    @objc private func openSettings() {
        let settingsViewController = SettingsViewController()
        navigationController?.pushViewController(settingsViewController, animated: true)
    }
}

private extension ProfileViewController {
    func setupUI() {
        setupViews()
        setupConstraints()
    }
    
    func setupViews() {
        view.addSubview(settingButton)
    }
    
    func setupConstraints() {
        settingButton.snp.makeConstraints { make in
            make.center.equalToSuperview()
        }
    }
}

But when I tap settingButton nothing happens.

I tried to set rootViewController like that on Scene Delegate:
window?.rootViewController = UINavigationController(rootViewController: TabBarController())

Also I tried here set ProfileViewController as a rootViewController

Also I tried with present method:

@objc private func openSettings() {
    let settingsViewController = SettingsViewController()
    present(settingsViewController, animated: true)
}