App dialogs not dismissing

### Describe the bug

In the example below:

- the window dialog works as expected
- the app dialog does not (more specifically it generally does not dismiss unless clicking the yes button rapidly for a while)

I suspect this is a bug?

### How to reproduce the bug

see code sample below

### Minimum example code

```shell
import toga

class App(toga.App):

def __init__(self):
super().__init__(formal_name='formal_name', app_id='app_id')

def startup(self):
main_window = toga.MainWindow()
main_window.show()
self.main_window = main_window

async def on_exit(self) -> bool:
question_dialog = toga.QuestionDialog('Exit?', 'Exit?')

# dialog in window context
# always seems to work
# return await self.main_window.dialog(question_dialog)

# dialog in app context
# mostly does not seem to work
# - clicking yes or no generally does not dismiss the dialog
# - clicking yes a lot of times in a fast manner strangely seems to dismiss the dialog after a while
# Python 3.14.0 | Toga 0.5.3 | Darwin 25.2.0
return await self.dialog(question_dialog)

app = App()
app.main_loop()
```

### Screenshots

_No response_

### Environment details

Python 3.14.0
Toga 0.5.3
~~Darwin 25.2.0~~ macOS 26

### Logs

```

```

### Additional context

_No response_

Start with the provided minimal example and reproduce the problem on macOS using Toga 0.5.3, focusing on App.on_exit() and the contrast between self.dialog() and self.main_window.dialog(). Trace the app-context dialog path and compare its dismissal handling with the window-context path. Done means the Yes and No buttons reliably dismiss the app dialog and return the expected result.

Written by the indexing model from the issue text.