Fix GitHub PyPI Build Pipeline

My Cython-based Python project lives on GitHub and already has a workflow file, but the build stage keeps failing, so the deploy step to PyPI never even runs. I need the workflow reviewed, corrected, and streamlined so it reliably builds wheels + sdist and then publishes them to PyPI―all in one push-tag-to-release flow.

The job is two-fold:

1. Restore a clean, repeatable build in GitHub Actions that handles Cython compilation and any standard package dependencies.
2. Wire the successful build to an automated deploy step that pushes to both TestPyPI and production PyPI using secure secrets.

Deliverables
• Updated workflow YAML committed via pull request, fully green on GitHub Actions
• Any supporting config tweaks (setup.py / pyproject.toml, MANIFEST.in, etc.) needed for a compliant package
• A concise explanation (Markdown or short call) showing what was wrong and why the final solution works

I’m comfortable editing code but new to the nuances of GitHub Actions, so clarity in the walkthrough matters as much as the fix itself. Keywords that may crop up in the solution include cibuildwheel, manylinux, twine, hatchling, or poetry—whatever you judge best for a robust build and deployment chain.

Once the pipeline succeeds end-to-end and I understand each change, the task is complete.