Standardize test filenames and Structure. Improve formatter diagnostics.

[sou-cheng-choi]

1. Standardize root unit-test filenames to the test_<area>_<topic>.py convention, while preserving all existing test functionality (fixtures, parametrization).
2. Change test file structure to object class based.
3. Implement a filename checker and enhance formatter tools
4. The scope is limited strictly to testing infrastructure and documentation, ensuring no changes to public APIs, numerical results, or core library code.