Problem

An agent can add a customer to the project from UI with only Service Desk Team role and creating customer account for that user at User Management is handled by the application. But in the case of API, the permission needed is Jira Administrator Global permission to create the customer and Service desk administrator permission to add the customer to a service desk project.
The Jira Service Desk Cloud REST API - Create Customer
The Jira Service Desk Cloud REST API - Add Customer

Why This Is Important

Giving Global level permission to create a portal-only customer (which is essentially adding a customer to the project) is not appropriate. Creating a portal only customer should require only Service desk administrator permission or adding the customer to the project through API should handle the create customer part.