You have already got the answer for the perfect result (=remove the wall and frame with precise background removal methods and insert a new clean background).
As you have already commented it is a hefty job. A simpler way is to paint a new background in the problematic area. It can be smoothed and patched afterwards for more plausible result.
Start by making a duplicate of the original image layer. Clone and paint there approximately the right greyshades over the frame and its shadows. I didn't try to paint gradients (a skilled airbrush user would make it), I only inserted dots of the different greys hoping they will be smoothed later. The green plant and the woodwork suffered a little in my not so perfect brushing, but that's not a problem:
Make with the polygonal lasso a selection which covers the painted area, but nothing of the green plant (or what's left of it) nor the other items below the frame. Apply Filter > Blur > Surface blur with so high radius and treshold that there's a gradient. Clone back with a small enough sharp edged 100% filling brush the destroyed parts from the original.
The blurred area has still well visible borders. Fade it with the healing brush - take the material from the blurred area. The result: