chore(format-tool-template): add clang-format configuration + format check

[SizzleUnrlsd]

Context

The codebase currently has no enforced formatting standard. This leads to inconsistent style, noisy diffs, and harder code reviews.

Goals

•	Add a versioned clang-format configuration to the repository.
•	Provide simple developer commands to format locally.
•	Add a CI check that fails when code is not formatted (CI should not auto-reformat).

Scope

1) Configuration

•	Add a .clang-format file at the repository root (or tools/format/ if that matches the repo conventions).
•	Pick a baseline style (e.g., LLVM / Google) and lock it in the config.

2) Developer commands

Add commands via Makefile / CMake targets / scripts:
• format: formats the whole C/C++ codebase in-place
• format-check: verifies formatting without modifying files

Expected behavior:
• format runs clang-format -i on all relevant sources
• format-check produces a non-zero exit code if any file differs from clang-format -style=file

3) CI

Add a CI job (e.g., GitHub Actions) named clang-format that:
• Installs clang-format
• Runs format-check
• Fails if formatting differences are detected

Proposed Implementation

Files to add

•	.clang-format
•	scripts/format.sh
•	scripts/format-check.sh
•	(Optional) update .gitignore if needed

File selection / exclusions

Target only:

•	*.c, *.cc, *.cpp, *.cxx, *.h, *.hh, *.hpp, *.hxx

Exclude common generated / external directories:

•	build/, external/, third_party/, vendor/, submodules/ (adapt to repo layout)

Acceptance Criteria

•	clang-format -style=file works from any subdirectory (config is discovered correctly)
•	./scripts/format.sh formats repository sources and does not touch external dependencies
•	./scripts/format-check.sh returns a non-zero exit code when at least one file is not formatted
•	CI fails when formatting is not respected
•	README or CONTRIBUTING documents how to install and use clang-format

Notes / Decisions

•	Standardize the clang-format version (e.g., 16 or 17) to avoid cross-version diffs between local and CI.
•	Suggested baseline style: BasedOnStyle: LLVM (adjustable).

Follow-ups (optional)

•	Add a pre-commit hook to run format-check before commits
•	Add a CMake target (cmake --build . --target format) if the project uses CMake