[3.13] gh-86608: Improve and restructure tarfile examples (GH-121771) (#136867)

gh-86608: Improve and restructure tarfile examples (GH-121771)

Add an example on how to write a tarfile to stdout; general improvements.
(cherry picked from commit cc81b4e501138b5793d419c81c3a2859a17207a7)

Co-authored-by: Dominic H <dom@dominic.sk>
Co-authored-by: Adam Turner <9087854+AA-Turner@users.noreply.github.com>