[3.13] gh-116742: Fix subprocess test_check_output_timeout() (GH-130836) (#130873)

gh-116742: Fix subprocess test_check_output_timeout() (GH-130836)

Fix a race condition in test_check_output_timeout() of
test_subprocess. Don't write into stdout anymore, since there is no
reliable way to synchronize the parent and the child processes.

Change the timeout from 3 seconds to 0.1 seconds, and remove
@requires_resource('walltime') decorator.
(cherry picked from commit 67a942d4272145ccdbdf4ceff31318e176f71355)

Co-authored-by: Victor Stinner <vstinner@python.org>