As of right now, the only way to pull the Org level audit logs located at admin.atlassian.com > Security > Audit log to another location is to use the organization REST API which is required to use the Org level API key for authentication and authorization.
The problem with it is that the Org level API key also grants full organization-level access where you can update organization settings and manage user accounts.
So, it would be beneficial to our customer if we can separate the permission to pull the Org level audit logs from any other Org level permissions and add the ability to grant read-only access to the logs using the API key.