faster shutter should improve sharpness. smooth press on the shutter button vs. jab helps too.

higher ISO = more noise = softness and less shadow details as well.

You didn't give us focal length on the zoom so a brief moment of shutter speed vs. focal length.

2x focal length = shutter speed should be adequate with a steady hand and still/slow moving objects. at 250mm x 1.6 (crop factor) = 1/400 A little lens move on a long focal length = blur. IS helps but it can't overcome significant camera movements ( I don't see this in the monkey shot - the blur would be in a direction) w/ a steady hand you could have ISO 200 ish which would make a difference in image quality. I don't like going above 800 and really prefer shooting at 100 or 200 if I at all can.

I am not convinced that the monkey shot is completely in focus. The Auto focus may have missed - not sure at f 5.6 though it should have been "close enough"

If this is a poor way to test autofocus accuracy I am sure someone will chime in. put the camera on a tripod or fixed surface. take a series of pictures using the autofocus, but change the focus by just a tiny bit between shots and see if the lens goes back to the 1st distance. Then shoot a 2nd series w/ manual focus and start a tiny bit short of what the autofocus picked and then work through the distance the autofocus picked.

Then on the compute peak at the pixels. Also shoot these series in RAW - too much image manipulation is going to JPG.

Best of luck