gh-104536: Improve `multiprocessing.process._cleanup` logic (#104537)

Fix a race condition in the internal `multiprocessing.process` cleanup
logic that could manifest as an unintended `AttributeError` when calling
`BaseProcess.close()`.

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Co-authored-by: Oleg Iarygin <oleg@arhadthedev.net>
Co-authored-by: Gregory P. Smith <greg@krypto.org>