Syncing and publishing what? What's so difficult about `git push` which pushes to GitHub and automatically deploys to Vercel? This doesn't look cool, but those two features are not going to be the ones I'll seek after.
Syncing the site data from builder to local fs and then building everything and configuring the app for publishing to vercel.
Just pushing to github only helps you if you only have static html/css if you wanted to publish a site as gh-page ... I guess you need to clarify your use case