Do I need to report neuroleptic malignant syndrome as a long-term health condition, or does it go away after being treated?

Yes, let doctor know. Even though a previous occurrence of nms has resolved, it may recur, especially if the causative agent, or one similar to it, is administered again. Let doctor know, so that a similar medication can be safely avoided.
Yes, definitely! If you have ever had nms, any new physician you see should be made aware. If a psychiatric medication caused it, then trying a new medication for the same problem might cause it to occur again so any new med should be started slowly and carefully. It is also an issue with anesthesia; we would avoid a drug called succinylcholine in anyone with a history of nms. Get a medicalert bracelet.
I'd mention it. Neuroleptics are used for many things beyond treating psychosis. We even used one commonly to treat nausea. While you seem to have recovered, it's good to know for future treatments.