Based on the picture, what do you recommend using to patch this hole?
I have done a lot of repairs like this, I usually use some kind of grinder or belt sander to bevel the edges of the area , then use hot mud to fill 3/4 of the depth once the hot mud is dry then I use mesh and mud to fill the remaining area and the mesh to bridge the gap (reduces cracking) after that I will sand and use topping mud for a quick final layer to match the existing surface, prime and cover paint is the last step. The res on the photo I can’t quite tell the pattern but matching is a bit easier if the base is solid, if you don’t use mesh or tape below the surface it WILL crack on those edges. Multiple layers something to bridge the edge below the surface and matching the texture on the top will make it look like a pro repair.