How to navigate from UIViewController -> SwiftUI View -> SwiftUI View -> UIViewController?

Screen 1 in UIViewController

import UIKit
import SwiftUI

class UIKitScreen1ViewController: UIViewController {
    
    var userData: UserData? // Data to be passed to next screen
    
    private let nameTextField = UITextField()
    private let emailTextField = UITextField()
    
    override func viewDidLoad() {
        super.viewDidLoad()
        
        // UI setup (name and email text fields)
        nameTextField.placeholder = "Enter Name"
        nameTextField.frame = CGRect(x: 50, y: 100, width: 300, height: 40)
        emailTextField.placeholder = "Enter Email"
        emailTextField.frame = CGRect(x: 50, y: 150, width: 300, height: 40)
        
        let nextButton = UIButton(type: .system)
        nextButton.setTitle("Next", for: .normal)
        nextButton.frame = CGRect(x: 50, y: 200, width: 100, height: 40)
        nextButton.addTarget(self, action: #selector(nextButtonTapped), for: .touchUpInside)
        view.backgroundColor = .white
        view.addSubview(nameTextField)
        view.addSubview(emailTextField)
        view.addSubview(nextButton)
    }
    
    @objc private func nextButtonTapped() {
        // Create a UserData object
        userData = UserData(name: nameTextField.text ?? "", email: emailTextField.text ?? "")
        
        // Navigate to Screen 2 (SwiftUI)
        let screen2 = UIHostingController(rootView: SwiftUIScreen2(userData: userData!))
        navigationController?.pushViewController(screen2, animated: true)
    }
}

struct UserData {
    let name: String
    let email: String
}

Screen 2 in SwiftUI

struct SwiftUIScreen2: View {
    @State var userData: UserData
    @State private var isNextScreenActive = false
    @State private var isUIKitNavbarHidden = false
    
    var body: some View {
        NavigationStack {
            VStack {
                Text("Name: \(userData.name)")
                Text("Email: \(userData.email)")
                
                Button("Go to Screen 3") {
                    isNextScreenActive = true
                }
                .padding()
                // Navigate to Screen 3
            }
            .navigationTitle("Screen 2")
            .navigationBarTitleDisplayMode(.inline)
            .navigationDestination(
                 isPresented: $isNextScreenActive) {
                     SwiftUIScreen3(userData: userData)
                      Text("")
                          .hidden()
                 }
        }
    }
}

Screen 3 in SwiftUI

struct SwiftUIScreen3: View {
    @State var userData: UserData
    @State private var isNextScreenActive = false
    
    var body: some View {
        NavigationStack {
            VStack {
                Text("Name: \(userData.name)")
                Text("Email: \(userData.email)")
                
                Button("Go to Screen 4") {
                    isNextScreenActive = true
                }
                .padding()
            }
            .navigationTitle("Screen 3")
            .navigationBarTitleDisplayMode(.inline)
            .navigationDestination(
                 isPresented: $isNextScreenActive) {
                     UIKitScreen4ViewControllerWrapper(userData: userData)
                      Text("")
                          .hidden()
                 }
        }
    }
}

Screen 4 in UIViewController

struct UIKitScreen4ViewControllerWrapper: UIViewControllerRepresentable {
    var userData: UserData

    func makeUIViewController(context: Context) -> UIKitScreen4ViewController {
        return UIKitScreen4ViewController(userData: userData)
    }

    func updateUIViewController(_ uiViewController: UIKitScreen4ViewController, context: Context) {
        // You can update the view controller here if needed (not necessary in this case)
    }
}

class UIKitScreen4ViewController: UIViewController {
    
    var userData: UserData
    
    private let nameLabel = UILabel()
    private let emailLabel = UILabel()
    
    init(userData: UserData) {
        self.userData = userData
        super.init(nibName: nil, bundle: nil)
    }
    
    required init?(coder: NSCoder) {
        fatalError("init(coder:) has not been implemented")
    }
    
    override func viewDidLoad() {
        super.viewDidLoad()
        
        // UI setup (name and email labels)
        nameLabel.text = "Name: \(userData.name)"
        nameLabel.frame = CGRect(x: 50, y: 100, width: 300, height: 40)
        emailLabel.text = "Email: \(userData.email)"
        emailLabel.frame = CGRect(x: 50, y: 150, width: 300, height: 40)
        
        view.addSubview(nameLabel)
        view.addSubview(emailLabel)
    }
}

I am facing double navigation bar issue where I can see UIKit's nav bar and SwiftUI's nav bar. I have looked everywhere online and I can't find solution for this issue due to navigationStack in swiftUI Double navigation bar issue

I also face issue with transition from screen 3(SwiftUI) to screen 4(UIViewController)

I can not figure out a way to make this flow work. I would really appreciate it if anyone can help me out.

I have tried hiding the Navigation bar when pushing the the swiftui hosting controller but navigation flow breaks when I reach the Screen4. Ultimately decided to post here for help

Since you're mixing UIKit and SwiftUI and trying to navigate between them, you need to remove NavigationStack because UIKitScreen1ViewController also has a navigationController. That's why it displays twice.

struct SwiftUIScreen2: View {
    var body: some View {
        NavigationStack { //<- need to be removed
            ...
        }
    }
}

navigationDestination only works within NavigationStack, thus replace it with NavigationLink like below:

struct SwiftUIScreen2: View {
    ...
    VStack {
        Text("Name: \(userData.name)")
        Text("Email: \(userData.email)")
        NavigationLink(destination: SwiftUIScreen3(userData: userData)) {
            Text("Go to screen 3")
        }
        .padding()
    }
    ...
}

Do it the same with SwiftUIScreen3. This is the output:

Another approach is wrapping all controllers into UIViewControllerRepresentable while holding a navigationPath. And you will have a single NavigationStack that navigates the flow through paths, as @workingdog mentioned.