check-style, doc: (fixes #1018) Update coding-style to use Doxygen @ tags and add check to check-style-clang-format.py

This MR proposes to fix #1018. Please see the discussion in that issue for details.

To Do

• Update coding-style.rst
• Add check to check-style-clang-format.py
• Refactor codebase
• Fix clang-tidy-diff errors: !1866 (merged), !1872 (merged), !2035 (merged)

Fix #1018