I need to add a page that an admin can access, with a list of inputs for various parameters (the parameters are related to non-WP functionality). The admin would be able to change these parameters whenever they want, click save, and then the values would need to be available via a REST service.
On what site are you working? The account you’re using to post here does not own any sites on WordPress.com.
This forum only provides end-user support for owners of free sites hosted on WordPress.com. We do not provide support in this forum for the WordPress.com REST API. Support for that API can be found at https://developer.wordpress.com/contact/
However, if you’re using the open source WordPress software at another host, then you want help with the WordPress REST API, rather than the WordPress.com REST API. In that case, please ask for help at https://wordpress.org/support/forums instead.