Nested dialog not visible after closing and reopening parent dialog

Nobody has claimed this yet.

### Bug explanation

When you close a parent dialog which has a nested dialog open, the nested dialog becomes invisible the next time you open the parent dialog, it prevents all input because only the nested dialog `PART_ContentCoverGrid` is visible:

https://github.com/user-attachments/assets/dab526c5-eae5-4ee2-98a3-2b884cadb849

This seems to work fine with `TransitionAssist.DisableTransitions="True"`:

https://github.com/user-attachments/assets/034231da-d54e-48c3-b3d8-89cd2375fa1d

Steps:

* Open `Root` dialog
* `Root` dialog opens `Inner` dialog
* Close `Root` dialog
* Reopen `Root` dialog

```csharp
public RootDialog RootDialog { get; } = new();

public MainWindow()
{
InitializeComponent();

_ = Application.Current.Dispatcher.InvokeAsync(async () =>
{
await Delay();
_ = DialogHost.Show(RootDialog);
await Delay();
RootDialog.OpenInnerDialog();
await Delay();

DialogHost.GetDialogSession(null)!.Close();

await Delay();
_ = DialogHost.Show(RootDialog);
});

static Task Delay() => Task.Delay(2000);
}
```

I'm not sure if this is even desired behavior, I assumed that all nested dialogs would close when parent is closed.
Hope I described the issue clearly, its a little bit hard to explain.

### Version

5.1.0

Start by reproducing the sequence in the issue with DialogHost.Show, a nested dialog, and transitions enabled; compare it with TransitionAssist.DisableTransitions="True". Trace DialogHost and nested-dialog state during parent close and reopen, then verify that the reopened parent no longer leaves only PART_ContentCoverGrid visible or blocks input.

Written by the indexing model from the issue text.