After we had a sliding glass door installed, we noticed that there was a gap alongside much of the edge of the door casing on the outer right side. This gap is widest in the center, and tapers back to normal as you go up or down the side. So it is more of a center bulge.

At its widest, by the lightswitch, the gap is about 1/8 inch. At the top and bottom where the gap is slight, the paint is only distorted a bit, but it breaks away from the wall where it is worst, revealing the gap. I can feel a bit of cooler air coming through at this widest point, so this needs to be fixed somehow.

I can push real hard on that panel it and seals the gap, but it returns to its bad state when I stop putting pressure on it. My plan is to trime away the ridge of lifted paint and then get some kind of wood filler to put in the crack. Then, after, I suppose I can perhaps caulk it, and add a bit of paint to replace the narrow strip I will have removed.

Does anyone have an idea how I should approach this repair? Not sure what to do here. Please offer suggestions.