getopts: cleanup, renames, remove reexports

* Remove public reexports, as a part of #19253
* Rename getopts::Fail_ to getopts::Fail
 * Didn't see a reason for the suffixed '_'
* Removed getopts::FailType
 * Looked like it was only beings used for tests; refactored the tests
   to stop requiring it
* A few other non-breaking trivial refactoring changes

[breaking-change]