why std::io uses a ReentrantMutex

From the readme:

> Figure out why std::io uses a ReentrantMutex so that we can find out whether we should too. parking_lot has one if needed.

This was added in https://github.com/rust-lang/rust/pull/24029 to allow locking stdout for the whole `print!()` without risk of deadlocking.

Start with the README passage and Rust pull request 24029, then inspect how this project currently handles stdout locking. Document why std::io uses a ReentrantMutex and conclude whether this project should use parking_lot's equivalent; done means the rationale and decision are recorded clearly.

Written by the indexing model from the issue text.