Make popover visible in accessibility tree in MacOS

I’m on macOS Monterey 12.4, XCode 13.3.1. Building a MacOS app in SwiftUI. I have a popover that displays when clicking on a button (for an example, open up the Apple Reminders app on Mac, click Add List and click on one of the Icon: images on the right. Notice the popup with many icons to choose from).

However, I cannot figure out how to make the popover part of the Accessibility Tree so I can emulate a click on it using UI Testing. What am I missing?

Here’s a simplified version of my code, which shows the issue:

private struct AStruct: Identifiable {
    let name: String
    var id: String { name }
}

private let someStructs: [AStruct] = [
    AStruct(name: "A"),
    AStruct(name: "B"),
    AStruct(name: "C"),
    AStruct(name: "D"),
    AStruct(name: "E")
]

struct ContentView: View {
    @State private var showingPopover = false
    
    var body: some View {
        HStack {
            Button {
                showingPopover = true
            } label: {
                Text ("Show Popup")
            }
            .accessibilityIdentifier("clickhere")
            .popover(isPresented: $showingPopover, arrowEdge: .bottom) {
                PopupMenu()
            }
            .padding()
        }
    }
}

struct PopupMenu: View {
    var body: some View {
        VStack(alignment: .leading, spacing: 0) {
            HStack(alignment: .top, spacing: 0) {
                ForEach(someStructs) { aStruct in
                    Button(action: {
                        print(aStruct.name)
                    }, label: {
                        Image(systemName: "circlebadge.fill")
                            .padding(EdgeInsets(top: 4, leading: 8, bottom: 4, trailing: 8))
                            .font(.title3)
                    })
                    .buttonStyle(PlainButtonStyle())
                }
            }
        }
        .padding()
    }
}

Here is the test case:

class Tests_macOS: XCTestCase {
    func test_ShowTree() throws {
        let app = XCUIApplication()
        app.launch()
        
        app.windows.buttons.element(matching: .button, identifier: "clickhere").click()
        print(app.debugDescription)
    }
}

And here is what the tree shows (menus omitted for brevity):

Element subtree:
 →Application, 0x10a704500, pid: 72192, title: 'TestPopupAccessibility', Disabled
    Window (Main), 0x10a705090, {{1126.0, 346.0}, {124.0, 80.0}}, identifier: 'TestPopupAccessibility.ContentView-1-AppWindow-1', title: 'TestPopupAccessibility', Keyboard Focused, Disabled
      Button, 0x10a7056e0, {{1142.0, 390.0}, {92.0, 20.0}}, identifier: 'clickhere', title: 'Show Popup'
      Button, 0x10a705810, {{1133.0, 352.0}, {14.0, 16.0}}, identifier: '_XCUI:CloseWindow'
      Button, 0x10a706ba0, {{1173.0, 352.0}, {14.0, 16.0}}, identifier: '_XCUI:FullScreenWindow'
      Button, 0x10a706cd0, {{1153.0, 352.0}, {14.0, 16.0}}, identifier: '_XCUI:MinimizeWindow'
      StaticText, 0x10a706e00, {{1193.0, 351.0}, {51.0, 16.0}}, value: TestPopupAccessibi...

I've tried modifying the accessibilityChildren, but I'm not even sure this is the right approach. The things i can find online are very sparse.

Make popover visible in accessibility tree in MacOS
 
 
Q