Welcome.
So, you need some backing, for that 2nd screw.
Were it I, and it isn't, I would remove the other screw and anchor, then the damaged area with a utility knife, cutting so the the cut edges are at about a 45 degree angle, then cut a piece of 1x2 about 2 or 2-1/2"'s longer than the vertical size of the cut-out, the using an 2-1/2 or 3" screw immersed into the 1x2, for maneuverability, insert the 1x2, centered, into the hole, then using 2, 1-5/8" screws, secure the 1x2 in place, next chamfer a piece of drywall, the size of the cut-out and secure it in place, then finish with some mastic or patching material, sand, prime and paint, then reattach you Curtin rod bracket.