daemon does not send unhandled exceptions to stdout/stderr

If I run `pub global run webdev daemon` to run a web app (I'm using [a copy of the Stagehand Angular sample](https://github.com/Dart-Code/Dart-Code/tree/rename-flutter-web-to-web/src/test/test_projects/web/broken) with [an exception added into the main dart file](https://github.com/Dart-Code/Dart-Code/blob/f66e8b275577011f362307f8ee62da9ee2933fdf/src/test/test_projects/web/broken/lib/src/todo_list/todo_list_component.dart#L37)) the exception is never printed in the daemon output.

This means when running from the IDE, the error never shows up in the debug console.

```
[{"event":"daemon.log","params":{"log":"[INFO] Debug service listening on ws://127.0.0.1:54984/qGXfwLlrIKI=\n"}}]
[{"event":"app.start","params":{"appId":"ShDLM17zRk4P+qJugvEy1w==","directory":"/Users/dantup/Dev/Dart-Code/src/test/test_projects/web/broken","deviceId":"chrome","launchMode":"run"}}]
[{"event":"app.started","params":{"appId":"ShDLM17zRk4P+qJugvEy1w=="}}]
[{"event":"app.debugPort","params":{"appId":"ShDLM17zRk4P+qJugvEy1w==","port":54984,"wsUri":"ws://127.0.0.1:54984/qGXfwLlrIKI="}}]

^C[{"event":"app.log","params":{"appId":"ShDLM17zRk4P+qJugvEy1w==","log":"Lost connection to device."}}]
[{"event":"app.stop","params":{"appId":"ShDLM17zRk4P+qJugvEy1w=="}}]
[{"event":"daemon.log","params":{"log":"[INFO] Stopped debug service on ws://127.0.0.1:54984\n"}}]
```

I think this works ok for Flutter web apps, but I think that could be because the Flutter framework catches all exceptions to print its own formatted errors.

Reproduce the issue with `pub global run webdev daemon` using the linked broken Angular sample and the exception in `todo_list_component.dart`. Trace how the daemon reports application output after startup; done means unhandled exceptions appear in the daemon's stdout/stderr or emitted app log so the IDE debug console can show them.

Written by the indexing model from the issue text.