Per this question on the FME forum:

https://community.safe.com/s/question/0D54Q00008bqqnFSAQ/how-can-i-allow-other-users-to-edit-my-fme-server-app

Please update the FME Server security model to allow alternate users (other than the original creator) to edit FME Server Apps without requiring "manage FME Server security permissions " permission.

The use case for this is to allow multiple users in a team to be able to make changes/edits to an FME Server App configuration.