Is there a CMS that has a Wordpress-like admin panel and content editing tools that builds and deploys the needed updates to a static site when you save an article, etc.?
Yes, there are lots now! There are some good ones, but some are definitely way pricier than I think they should be. With Next.js, you can even use Wordpress as a cms to back a static blog (https://github.com/vercel/next.js/tree/canary/examples/cms-w...)