https://en.wikipedia.beta.wmflabs.org/api/rest_v1/#/Citation/getCitation

just returns a bunch of hyperswitch errors when you try to make requests.

A quick work around would be just to configure the Citoid extension in VE (via localsettings.php) to use the live endpoint rather than a "beta" version so it works for testers with $wgCitoidFullRestbaseURL

Restbase is being decommed anyway so there's probably no point in trying to get it the restbase endpoint to work on beta.