Multiprocess operations can lead to spinner deadlock
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### 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
```
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