A user must have any of these 3 Entra ID roles to have permission to create and manage Enterprise Applications:
Application Administrator
Cloud Application Administrator
Global Administrator
One can verify that one have one of these roles with this click route that shows how to go about it for the role Application Administrator:
Here is the same route verbose:
Sign in to the Azure portal at http://portal.azure.com
Search for Entra ID in the search bar and select it from the search result.
Select Roles and administrators from the vertical menu.
Click on the 3 roles one by one to see if the user’s name appear listed. If it does for at least one of them, then the user has the required permission.