I am just getting started with integrating Rancher into Azure pipelines by setting up a service connection to a container registry on Rancher. Previously when using IMB Cloud, there was a publicly exposed endpoint for the IBM Cloud Container Registry API (us.icr.io for Dallas). After reviewing the docs for Rancher, I didn't find an Endpoint for a Rancher Cloud Container Registry API. Is there one that exists?
Rancher is something you install on your hardware and not a "cloud". There is no registry built-in, though you can install something like Harbor on to a cluster and use it. The docs you're linking to are to an ancient version of 1.x that is no longer maintained or supported and nobody should be using. You should be looking at 2.5.x today.