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[CI] Enable clang-format check
Description
According to the discussion in issue #580, this PR adds a job in CI to check code formatting using pre-commit with clang-format v19.1.0.
This PR will be rebased after PR #594 is merged. We should have a green clang-format check then.
Fixes #580
Checklist
All Submissions
- Do all unit tests pass locally? No changes that affect tests.
- Have you formatted the code using clang-format? N/A