[clang-tidy][NFC] Update contribution guide for test language standards (#184769)

Explain how to use the `-std` flag in clang-tidy tests and reorganize
the content on C++ pitfalls into a new subsection for better
readability.

Related discussion: https://github.com/llvm/llvm-project/pull/184741

As of AI Usage: the documentation is partially rephrased by Gemini 3.

GitOrigin-RevId: ca2b4db828bb48aefd756c774ee3f071d821c8ff