Changing `NotifyIcon.Icon` for a registered `NotifyIcon` does not work

Describe the bug

Changing NotifyIcon.Icon for a registered NotifyIcon does not work.

The icon on the tray remains the default app icon.

To Reproduce

using WinIcon = System.Drawing.Icon;

    private static WinIcon? GetIcon(string fileName)
    {
        return WinIcon.ExtractAssociatedIcon(fileName);
    }

    private static ImageSource? GetIconImage(string fileName)
    {
        using var icon = GetIcon(fileName);
        if (icon != null)
        {
            return Imaging.CreateBitmapSourceFromHIcon(
                        icon.Handle,
                        new Int32Rect(0, 0, icon.Width, icon.Height),
                        BitmapSizeOptions.FromEmptyOptions());
        }
        return null;
    }

    private void UpdateIcon(object sender, PropertyChangedEventArgs e)
    {
                RootTitleBar.Tray.Icon = RootTitleBar.Icon = Icon = GetIconImage(Paths.GetAppFile());
    }

Where RootTitleBar is declared as:

        <wpfui:TitleBar x:Name="RootTitleBar" Grid.Row="0">
            <wpfui:TitleBar.Tray>
                <wpfui:NotifyIcon>
                </wpfui:NotifyIcon>
            </wpfui:TitleBar.Tray>
        </wpfui:TitleBar>

Expected behavior

The tray icon should change when UpdateIcon is called.

Screenshots

No response

OS version

Windows 11 22H2

.NET version

.NET 6.0.401

WPF-UI NuGet version

2.0.3

Additional context

No response

Start at the NotifyIcon registration and Icon property update path, then reproduce the issue with the provided WPF example on Windows. Verify that changing RootTitleBar.Tray.Icon after registration updates the displayed tray icon instead of retaining the default app icon.