When you build a react app, the files at folder build contains everything it needs to run
If your hosting server hasn't integration with CI/CD, then you must deploy manually only the build folder, not the root folder (the folder that contains package.json).
I believe your issue is just a confusion/misunderstanding on how react works, how to deploy it, and how to run it.
React needs to be built on an environment where node, npm, and other tools are available. It can be on a build server or in your local machine.
After built, react app is just a folder with a bunch of html, css, js files which will run on the client browser, so, there's no dependency on NODE anymore.
These static files must be served with a simple static file server (apache, nginx, iis, etc),
I recommend you build the app locally on your machine and then deploy manually to your host through ftp, ssh or web interface.
If react is overkill to your needs, then don't use it.
The best approach is to host it in a cloud service that can do the full CI/CD integrated with git, all automated (Google GCP, AWS, Azure, Netlify, etc)