[3.11] gh-106368: Increase Argument Clinic CLI test coverage (GH-107156) (#107190)

Instead of hacking into the Clinic class, use the Argument Clinic tool
to run the ClinicExternalTest test suite.

(cherry picked from commit 83a2837)

Co-authored-by: Erlend E. Aasland <[email protected]>
Co-authored-by: Nikita Sobolev <[email protected]>

Author: 3 people