Everything works well in development.
When I push on GitHub, it triggers the action and deploy on production. GitHub says the deployment succeed.
The problem comes from the built folder that is not generated by ghost so the CSS is not loaded.
Do you mean that your theme isn’t built before being deployed (bundling, minifying)?
The GitHub theme deploy action isn’t responsible for that. You either need to build those assets before pushing to your repository or set up another GitHub action that builds the assets before they are deployed.