Not sure if another opinion is welcome, and obviously it’s coming from a WordPress developer, so maybe I have a different point of view (and probably don’t have all the information), but It actually sounds like you’d actually be better just doing it all in WordPress.
That would eliminiate the need for any kind of OAuth anything, because you could just use native WP credentials everywhere. There are plugins around that let you handle subscription-based content, and there are a few popular shopping cart/store plugins that can help you do the commerce side of things as well.
All of that failing, I think you could use Keyring to handle just the communication part of things (since it can handle signing requests etc), although it’s probably overkill. If you’re doing your own implementation, in a single environment, you’re probably better off installing the PECL OAuth package (https://pecl.php.net/package/oauth) and then using that, since you can guarantee a single, known implementation of a consistent version of OAuth across all services. Keyring is best when you need to work with different authentication types (OAuth1 + 2, HTTP Basic etc), and when you need to be more portable (so can’t guarantee Pecl/some specific library).
Hope that helps with your decision!