SwiftUI NavigationSplitView like Apple Music

In the Apple Music app on iPad (horizontal size class == .regular), when a selection is made from the Split View sidebar, the detail switches to a separate UINavigationController for that selection, where we can push/pop views. If we make a different selection from the sidebar, we get another UINavigationController to manipulate. If we return to the first selection, the detail view is still showing the stack contents for that controller.

I am trying to get the same behavior from NavigationSplitView in SwiftUI, but the detail view will reset its presented controller to its root. I think this is because NavigationSplitView uses whatever NavigationStack it finds in the detail hierarchy to manage its contents, effectively erasing the per-view stack contents. I have tried various methods of saving and restoring the navigation path without any luck. Any ideas on how to approach this?

I have included a very simple example to show what I'm talking about.

import SwiftUI

struct ExampleView: View {
  enum Selection: String, CaseIterable {
    case letters
    case numbers
  }
  
  @State private var selection: Selection?
  
  var body: some View {
    NavigationSplitView {
      List(selection: $selection) {
        ForEach(Selection.allCases, id: \.self) { selection in
          NavigationLink(value: selection) {
            Text(selection.rawValue.capitalized)
          }
        }
      }
      .navigationTitle("Sidebar")
      
    } detail: {
      switch selection {
      case .letters:
        self.lettersView
        
      case .numbers:
        self.numbersView
        
      default:
        Text("Make a selection")
      }
    }
  }
  
  var lettersView = LettersView()
  var numbersView = NumbersView()
}

struct ExampleView_Previews: PreviewProvider {
  static var previews: some View {
    ExampleView()
  }
}

// MARK: -
struct LettersView: View {
  private let letters = ["a", "b", "c", "d", "e", "f"]
  @State private var path = NavigationPath()
  
  var body: some View {
    NavigationStack(path: $path) {
      List {
        ForEach(letters, id: \.self) { letter in
          NavigationLink(value: letter) {
            Text(letter.uppercased())
          }
        }
      }
      .navigationTitle("Letters")
      .navigationDestination(for: String.self) { letter in
        Text(letter.uppercased()).font(.largeTitle)
      }
    }
  }
}

// MARK: -
struct NumbersView: View {
  private let numbers = Array(0..<6)
  @State private var path = NavigationPath()
  
  var body: some View {
    NavigationStack(path: $path) {
      List {
        ForEach(numbers, id: \.self) { number in
          NavigationLink(value: number) {
            Text(String(number))
          }
        }
      }
      .navigationTitle("Numbers")
      .navigationDestination(for: Int.self) { number in
        Text(String(number)).font(.largeTitle)
      }
    }
  }
}