[BE] Refactoring test execution and improving comments (#99467)
Sharing code between the code that handles test results in parallel vs serial mode.
Note that the original version of this code had an inconsistency between the two versions where it would execute `print_to_stderr(err_message)` on every test that ran in parallel, but for serial tests it would only invoke `print_to_stderr(err_message)` if `continue_on_error` was also specified. By sharing code, this PR changes that behavior to be consistent between the two modes.
Also adding some comments.
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### <samp>🤖 Generated by Copilot at 029342c</samp>
> _Sing, O Muse, of the skillful coder who refined_
> _The PyTorch testing script, `run_test.py`, and shined_
> _A light on its obscure logic, with docstrings and comments_
> _And made it run more smoothly, with better error contents_
Pull Request resolved: https://github.com/pytorch/pytorch/pull/99467
Approved by: https://github.com/huydhn, https://github.com/malfet
