UIAimatedNavigationTransition с UIKit и SwiftUI

вам нужно создать аниматора и делегата перехода

    import UIKit

    class Animator: NSObject, UIViewControllerAnimatedTransitioning {

       func transitionDuration(using transitionContext: UIViewControllerContextTransitioning?) -> TimeInterval {
        return 0.5
       }

       func animateTransition(using transitionContext: UIViewControllerContextTransitioning) {
        guard let fromVC = transitionContext.viewController(forKey: .from),
              let toVC = transitionContext.viewController(forKey: .to) else {
            return
        }

        let containerView = transitionContext.containerView

        containerView.addSubview(toVC.view)
        toVC.view.frame = fromVC.view.frame
        toVC.view.alpha = 0.0

        UIView.animate(withDuration: transitionDuration(using: transitionContext), animations: {
            toVC.view.alpha = 1.0
        }) { finished in
            fromVC.view.removeFromSuperview()
            transitionContext.completeTransition(finished)
        }
       }
}

import UIKit

class TransitioningDelegate: NSObject, UIViewControllerTransitioningDelegate {
    func animationController(forPresented presented: UIViewController, presenting: UIViewController, source: UIViewController) -> UIViewControllerAnimatedTransitioning? {
        return Animator()
    }

    func animationController(forDismissed dismissed: UIViewController) -> UIViewControllerAnimatedTransitioning? {
        return Animator()
    }
}

затем примените делегат перехода к контроллеру представления хоста пользователя в файле контроллера представления при нажатии кнопки

//MARK: - Properties
let transitionDelegate = TransitioningDelegate()

//MARK: - Button Action
@objc func showSwiftUIView() {
    let swiftUIView = SwiftUIView()
    let hostingController = UIHostingController(rootView: swiftUIView)
    hostingController.modalPresentationStyle = .fullScreen
    hostingController.transitioningDelegate = transitionDelegate
    present(hostingController, animated: true, completion: nil)
}