There are indeed many ways to treat patients with permanent facial palsy. Broadly speaking, treatments could be divided into static and dynamic reconstructions.
Static reconstruction aims to improve static symmetry at rest, e.g. by lifting the angle of mouth. The surgery is shorter and simpler but they do not restore muscle functions, i.e. patients still cannot smile after surgery. Dynamic reconstruction surgeries (e.g. gracilis muscle transfer) are more complicated but tend to have better results. These procedures improve symmetry at rest and can potentially reanimate the face as well. It gives patients a chance to smile with their paralyzed face again (with some training after surgery).
Each treatment option has its own advantages, limitations, and risks. You are advised to seek professional opinion and assessment to see which option suits you best.