Try finding a cognito user from a cognito identity, you can't.
Visit the amplify-js and amplify-cli github repos and search for cognito issues.
Try using the cognito console, it is a litter box of warning messages and exceptions. Try connecting Cognito and Pinpoint if you are in Europe, 2 years and it still doesn't work, but no indication.
See its cloudformation configuration and how many field changes cause a Replace. Yes, replace Cognito and goodbye users.
Until recently user names were case sensitive, and they didn't have basic account enumeration protections.
Its UX is exactly how DynamoDB can do damage to a product.