Create a department.

Adds one department, with the same rules as adding a department in the AwardSpring admin interface: the name is required and must not already be used by another department at the institution, ignoring upper and lower case and spaces at either end. A new department starts with the same settings the admin interface gives one. Departments are not available on every plan; on a plan without them this returns 403 permission_required.

Idempotency: the request supports an optional Idempotency-Key header (any printable-ASCII string, 1–255 chars — UUIDs work well). When supplied, the same key plus the same request body within 24 hours returns the original response verbatim without creating a duplicate department. The same key with a different body returns 422 idempotency_key_request_mismatch; a concurrent retry while the first call is still executing returns 409 idempotency_key_in_flight.