Speed up logging once again (#9981)

* Update `tracing`-related dependencies

* Enable `parking_lot` feature in `tracing-subscriber`

* Add an asynchronous stderr logger

* Make clippy happy

* Add an integration test for the logger

* Refactor `test_logger_filters`'s subprocess machinery into a separate function

* Use a child process instead of hooking into stderr for the test

* Add a doc comment for `MakeStderrWriter`

* Move the initialization into the `MakeStderrWriter`'s constructor

* Add an extra test case to trigger the logger's emergency flush mechanism

* Use the buffer's mutex for asynchronous flushes

* Remove vestigial `nix` dependency from one of the previous commits