Rework Argument Clinic error handling

[erlend-aasland]

Suggesting to...:

• Introduce ClinicError and ClinicWarning
• Rework fail to raise a ClinicError, and warn to use warnings.warn(..., ClinicWarning)

This will simplify the test suite (we can use assertRaisesRegex instead of the current capture stdout hacks). Proof-of-concept implementation: https://github.com/Argument-Clinic/cpython/pull/2

[erlend-aasland]

This was addressed in #107467, #104683. Closing as outdated.