Use overlay with animation
Parent view
struct ContentView: View {
    @State var isShowSheet: Bool = false
    
    var body: some View {
        VStack{
            Button("Show Sheet") {
                withAnimation {
                    isShowSheet.toggle()
                }
            }
        }
        .frame(minWidth: 0, maxWidth: .infinity, minHeight: 0, maxHeight: .infinity)
        .overlay(isShowSheet ? FullScreen(isShowSheet: $isShowSheet.animation()) : nil)
    }
}
FullScreen view
struct FullScreen: View {
    
    @Binding var isShowSheet: Bool
    
    var body: some View {
        Color.blue
            .transition(.move(edge: .leading))
            .onTapGesture {
                isShowSheet = false
            }
            .edgesIgnoringSafeArea(.all)
    }
}

The second option is to use UIViewController with custom animation.
I have use viewControllerHolder extesion from this link (// https://stackoverflow.com/a/58494173/14733292) and added CATransition()
struct ViewControllerHolder {
    weak var value: UIViewController?
}
struct ViewControllerKey: EnvironmentKey {
    static var defaultValue: ViewControllerHolder {
        return ViewControllerHolder(value: UIApplication.shared.windows.first?.rootViewController)
    }
}
extension EnvironmentValues {
    var viewController: UIViewController? {
        get { return self[ViewControllerKey.self].value }
        set { self[ViewControllerKey.self].value = newValue }
    }
}
extension UIViewController {
    func present<Content: View>(style: UIModalPresentationStyle = .automatic, @ViewBuilder builder: () -> Content) {
        let toPresent = UIHostingController(rootView: AnyView(EmptyView()))
        toPresent.modalPresentationStyle = style
        toPresent.rootView = AnyView(
            builder()
                .environment(\.viewController, toPresent)
        )
        self.presentController(toPresent)
    }
    
    func presentController(_ viewControllerToPresent: UIViewController) {
        let transition = CATransition()
        transition.duration = 0.25
        transition.type = CATransitionType.push
        transition.subtype = CATransitionSubtype.fromLeft
        self.view.window?.layer.add(transition, forKey: kCATransition)
        
        present(viewControllerToPresent, animated: false)
    }
    
    func dismissController() {
        let transition = CATransition()
        transition.duration = 0.25
        transition.type = CATransitionType.push
        transition.subtype = CATransitionSubtype.fromRight
        self.view.window?.layer.add(transition, forKey: kCATransition)
        dismiss(animated: false)
    }
}
ContentView and FullScreen
struct ContentView: View {
    @Environment(\.viewController) private var viewControllerHolder: UIViewController?
    
    var body: some View {
        VStack{
            Button("Show Sheet") {
                viewControllerHolder?.present(style: .overFullScreen, builder: {
                    FullScreen()
                })
            }
        }
        .frame(minWidth: 0, maxWidth: .infinity, minHeight: 0, maxHeight: .infinity)
    }
}
struct FullScreen: View {
    
    @Environment(\.viewController) private var viewControllerHolder: UIViewController?
    
    var body: some View {
        Color.blue
            .onTapGesture {
                viewControllerHolder?.dismissController()
            }
            .edgesIgnoringSafeArea(.all)
    }
}
