Multiprocess operations can lead to spinner deadlock

### Bug Description

There is a bad interaction between the way we perform overlay operations (a chroot in a multiprocess-created subprocess) and the way craft applications indicate progress on the cli (a spinner in a thread).

The consequence of the bad interaction is that trying to write an info message to the terminal ends up deadlocking the main thread in the subprocess because the thread that could unblock it does not exist.

See https://github.com/canonical/craft-parts/pull/535.

### To Reproduce

TODO

### part yaml

_No response_

### Relevant log output

```shell
TODO
```

Start by reading the linked craft-parts PR 535 and tracing the overlay/chroot subprocess path together with the CLI spinner thread. Reproduce the TODO scenario involving an info message, then verify that writing it no longer deadlocks the subprocess.

Written by the indexing model from the issue text.