chore(ci): Use pre-commit checks in CI

[ZacBlanco]

What problem does this PR solve?

Use pre-commit checks as CI jobs to prevent relying on pre-commit checks locally. There have already been some PRs which break the formatting rules in the pre-commit checks introduced by #113

Type of Change

• 🐛 Bug fix (non-breaking change which fixes an issue)
• ✨ New feature (non-breaking change which adds functionality)
• 🚀 Performance improvement (optimization)
• ⚠️ Breaking change (fix or feature that would cause existing functionality to change)
• 🔨 Refactoring (no logic changes)
• 🔧 Build/CI or Infrastructure changes
• 📝 Documentation only

Description

Removes the individual clang-format and license-check workflows in favor of just calling pre-commit run --all-files to verify all pre-commit checks succeed in the codebase. This prevents needing to maintain multiple workflows for the new checks separate from our pre-commit-config.yaml and also ensures that all new changes follow the pre-commit guidelines defined in the config.

Performance Impact

• No Impact: This change does not affect the critical path (e.g., build system, doc, error handling).
• Positive Impact: I have run benchmarks.
• Negative Impact: Explained below (e.g., trade-off for correctness).

Release Note

N/A

Checklist (For Author)

• I have added/updated unit tests (ctest).
• I have verified the code with local build (Release/Debug).
• I have run clang-format / linters.
• (Optional) I have run Sanitizers (ASAN/TSAN) locally for complex C++ changes.
• No need to test or manual test.

Breaking Changes

• No
• Yes (Description: ...)

[yangzhg]

LGTM

[ZacBlanco]

@yangzhg thanks for your previous comments and improvements by creating license_check.go. I have made a few more improvements to it by using license-eye directly as a library. I also fixed the caching in CI. This check now runs in ~3 minutes when the pre-commit environment is cached. Please take one more pass when you have some time