Error messages should be sent to stderr instead of stdout.

If the supplied arguments aren't parseable and a usage message is output, it should go to stderr, not stdout. (Whereas if the user requested a usage message with the -help option, that should go to stdout.). This is standard behavior for command-line tools running in a POSIX environment.

Start by locating the argument-parsing path that emits the usage message and the existing tests for -help and invalid arguments. Confirm the current output streams, then add coverage showing invalid input uses stderr while -help uses stdout; done means those tests pass.

Written by the indexing model from the issue text.