Cannot find Element in WinForm Embedded WebView2 with UIAutomation

[KiYugadgeter]

I would like to push button in WinForm embedded WebView2 with UIAutomation.
But cannot find it despite it can see with inspect.exe.

It cannot see not only AutomationElement::FindAll but also enumeration using TreeView.

I want find a element that has name is "ログイン" (because Japanese stock trade software, I would like to push login button programatically)

I have no idea whether my code bug or problem of WebView2 such like #3530

The following is code:

void findAndPushLoginButton(Process? proc)
{

    var cond = new PropertyCondition(AutomationElement.NameProperty, "ログイン");
    var cond2 = new PropertyCondition(AutomationElement.AutomationIdProperty, "WebAuthentication");
    var cond3 = new PropertyCondition(AutomationElement.ProcessIdProperty, proc.Id);
    var loginwindow = AutomationElement.RootElement.FindFirst(TreeScope.Children, new AndCondition(cond, cond2, cond3));
    
    elementstack.Push(loginwindow);

    var rawViewWalker = TreeWalker.RawViewWalker;
    AutomationElement? res = null;
    while (elementstack.Count != 0)
    {
        var e = elementstack.Pop();
        var nameobj = (string)e.GetCurrentPropertyValue(AutomationElement.NameProperty);
        var ct = e.GetCurrentPropertyValue(AutomationElement.ControlTypeProperty);
        var framework_id = e.GetCurrentPropertyValue(AutomationElement.FrameworkIdProperty) as string;
        var automation_id = e.GetCurrentPropertyValue(AutomationElement.AutomationIdProperty) as string;
        var classname = e.GetCurrentPropertyValue(AutomationElement.ClassNameProperty) as string;
        var actual_ct = ct as ControlType;
        Console.WriteLine("name={0}, ctrltype={1}, automation_id={2}", nameobj, actual_ct?.ProgrammaticName, automation_id);

        if (nameobj == "ログイン" && framework_id == "Chrome") 
        {
            res = e;
            Console.WriteLine("Button is found");
            var loginButton = res.GetCurrentPattern(InvokePattern.Pattern) as InvokePattern;
            loginButton?.Invoke();
            return;
        }
        var sib = rawViewWalker.GetNextSibling(e);
        if (sib != null)
        {
            elementstack.Push(sib);
        }
        var firstchild = rawViewWalker.GetFirstChild(e);
        if (firstchild != null)
        {
            elementstack.Push(firstchild);
        }

    }
    if (res == null)
    {
        Console.WriteLine("Button is not found");
    }
}