[3.13] gh-141930: Use the regular IO stack to write .pyc files for a better error message on failure (GH-141931) (#142023)

* Use open() to write the bytecode
* Convert to unittest style asserts
* Tweak news, thanks @vstinner
* Tidy
* reword NEWS, avoid word "retried"
(cherry picked from commit 656a64b37f817cc8fe36ee17f332100482185cce)

Co-authored-by: Stefano Rivera <stefano@rivera.za.net>