fix: Update CI badges and improve Codecov integration

- Fix broken badges in README.md by using correct GitHub Actions paths
- Update CI workflow to use Codecov v4.0.1 with proper configuration
- Replace static coverage badge with dynamic Codecov badge
- Add proper repository slug and token configuration for coverage upload
- Remove non-existent workflow badges that were causing 404 errors

This ensures badges display correctly and coverage reporting works properly.

Author: trumpchifan