The Lambda authorizer's authorization caching might be using an outdated policy based on the previous Engineering attribute.

Caching on the Amazon Cognito user pool could be involved, but this is less likely the direct cause of the department value issue.

A missing Department tag on the Lambda authorizer's IAM role might affect access control but isn't the main reason for the incorrect department reporting.

A missing Department tag on the Amazon Cognito user pool's IAM role isn't the primary cause of the caching issue with the user's department attribute.