According to the documentation ProForma developer documentation a user must have the ProForma: Export All Data global permission to perform data exportation.

Export Data API

In order to access the ProForma Export API, a user must have the ProForma: Export All Data global permission (Jira Settings > Systems > Global Permissions). No groups are assigned to this permission by default. Once this permission is given, members of the group will be able to call export APIs in ProForma with full access to all form and issue data.

Customer would like to use the Project Permission scheme instead of ProForma: Export All Data global permission to set granular permissions for this API call by Project.

In other words, if allows users to access the API call through the ProForma: Export All Data global permission, anyone can pull data from any project whatsoever.