Hello. The Authenticated version of the Eligibility API is currently only restricted to short-lived user tokens which are explicitly authorized for a TIN. Registry tokens currently do not have the capability to utilize the Authenticated Eligibility API by design per CMS security requirements.
However, there are initiatives that are currently in development by various teams that will enable users to explicitly grant permissions to various applications to act on their behalf. The tokens issued for an application on behalf of a user would then be able to interact with secure Eligibility API components. There is no current timeline for that initiative, but teams will keep this Google Group informed of updates.
Chris