The `tree_source` example is problematic

### Describe the bug

The `tree_source` example creates a lazy-loading tree view of the current directory.

1) When used with Briefcase (`dev` or `run`), the `cwd` is `$HOME`.....the app loaded 10GB in to memory before i killed it
2) It doesn't seem to actually be lazy.....it tried to read my entire home directory before showing the window
3) It completely bombs out on a node if anything causes an `OSError`...for instance, a broken symlink in my home dir

### Steps to reproduce

Run `briefcase dev` for the `tree_source` example

### Expected behavior

The directory used for the tree is enforced to be the directory of the app and it is actually lazy.

### Screenshots

_No response_

### Environment

- Operating System: pop os 22.04
- Python version: 3.10.12
- Software versions:
- Briefcase: `0.3.15.dev361+g02f412be.d20230619`
- Toga: `0.3.2.dev383+g7d68e74d.d20230619`

### Logs

_No response_

### Additional context

_No response_

Start with the `tree_source` example and reproduce it with `briefcase dev`, checking how it chooses the directory, loads children, and handles `OSError`. Done means the example stays scoped to the app directory, loads directory contents lazily, and does not fail when a node raises an `OSError`.

Written by the indexing model from the issue text.