chore(pre-commit hook): Add `clang-format` check to `pre-commit` hook

[SizzleUnrlsd]

Description

We should enforce a consistent C/C++ code style by running clang-format as part of the Git pre-commit hook. This prevents unformatted code from being committed and reduces review noise.

Goals

• Ensure all staged C/C++ sources are formatted according to the project’s .clang-format.
• Fail the commit if formatting is required (or optionally auto-apply formatting and re-stage).
• Keep the hook fast and only operate on staged files.

Proposed implementation

• Integrate clang-format into the existing pre-commit workflow (e.g., via pre-commit framework).
• Use .clang-format at repo root as the single source of truth.
• Run only on relevant file extensions:
  • *.c, *.h, *.cc, *.cpp, *.cxx, *.hpp, *.hxx, *.inl
• Operate only on staged files (avoid scanning the full repo).

Suggested behavior (pick one)

1. Check-only (recommended for CI parity)

• Run clang-format and fail if the output would change files.
• Print the list of files requiring formatting and how to fix:
  • clang-format -i <files> (or pre-commit run -a)

2. Auto-fix

• Run clang-format -i on staged files, then re-stage modified files.
• Commit proceeds if everything is formatted.

Acceptance criteria

• Committing unformatted C/C++ code is blocked (or auto-fixed) by the hook.
• Hook runs in reasonable time on typical commits (only staged files).
• Works on macOS and Linux (and ideally Windows if supported).
• Clear developer instructions are added to CONTRIBUTING.md (or equivalent).

Tasks

• Add clang-format hook to .pre-commit-config.yaml (or hook scripts if not using pre-commit config).
• Ensure .clang-format is present and documented (or add it if missing).
• Restrict hook to staged C/C++ files only.
• Add documentation in CONTRIBUTING.md (install + how to run manually).
• Add a small test/CI job (optional) that runs pre-commit run --all-files to keep CI consistent.

Notes

• Prefer using clang-format from a pinned LLVM/clang toolchain version (or document the required minimum version) to avoid formatting diffs across environments.