[3.13] gh-141473: Fix subprocess.Popen.communicate to send input to stdin upon a subsequent post-timeout call (GH-141477) (#142060)

* gh-141473: Fix subprocess.Popen.communicate to send input to stdin upon a subsequent post-timeout call (GH-141477)

* gh-141473: Fix subprocess.Popen.communicate to send input to stdin
* Docs: Clarify that `input` is one time only on `communicate()`
* NEWS entry
* Add a regression test.

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(cherry picked from commit 526d7a8bb47bd8ff58c829c30384cd70cc5d0747)

Co-authored-by: Artur Jamro <artur.jamro@gmail.com>
Co-authored-by: Gregory P. Smith <greg@krypto.org>

* no assertStartsWith

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Co-authored-by: Artur Jamro <artur.jamro@gmail.com>
Co-authored-by: Gregory P. Smith <greg@krypto.org>