Is the remaining numbness in the chin/lower lip (a year after jaw surgery and sliding genioplasty) permanent, or could it still improve?

Yes. It is unlikely to return to normal this late after surgery but it could still improve, especially if you have noticed any return over the last several months. Tingling is a sign of healing.
Most Likely Will Not. Although very rare, I have seen patients who have had sensation recovery beyond a year. There are several injuries to a nerve that can occur. Neuropraxia, axonotmesis, and neurotmesis. Best to discuss this with your oral and maxillofacial surgeon.