Following up on my previous comment...
From the site settings page in Chrome (chrome://settings/content/all), I deleted all site data and permissions for apple.com. I next went back to the Cloudkit dashboard page and refreshed it, but I still got the error message. So I pressed the "Sign out" button there, and then signed back in. It is now working again for me from a regular (non-incognito) Chrome window.
Topic:
App & System Services
SubTopic:
iCloud & Data
Tags: