In on-premises when user trying to delete a record the pop up message is clear and user friendly saying that the user doesn't have respective privileges to delete.
Whereas In the cloud environment, when a user with CRM full role access trying to delete a record from any entity getting the pop up message in the below format
Message: {0} with id {1} does not have {2} right(s) for record with id {3} of entity {4}. Consider assigning a role with the required access level to the user or team. For further troubleshooting, please work with a system administrator to use the Access Checker tool on this record: {5}. More details: {6}
Error code for reference:0x80048306
The error message in pop up dialog is clear in on-prem where as in cloud the message is more and not clear. Since it is a standard behavior, Please create a feature to edit the error message the users are getting.