GH-122679: Add `register()` to argparse docs (#126939)

* Add register() to argparse docs

* Add newline

* Formatting

* Fix codeblock

* Move section

* Add signature

* Add newline

* Fix indent

* Fix indent take 2

* Rephrase

* Simplify language

* Address PR comments

* Add references to register in type and action

* Remove unnecessary reference

* Rephrase and add success case