No—some change in sharpness between apertures can be normal, but obvious blur or a doubled look at f/4 is not. Based on the description, this looks less like autofocus error and more like an optical issue.

A common cause is a filter on the front of the lens, especially a poor-quality or damaged one, which can introduce ghosting, softness, or misalignment that becomes more noticeable wide open. Remove any UV/protective filter and test again.

Less likely, but still possible, are motion blur or stabilization-related issues. In Aperture Priority, opening to f/4 usually gives a faster shutter speed, so motion blur would normally be reduced, but it's still worth testing on a tripod or with steady support.

If the problem remains with no filter attached, the lens may have an optical defect or element misalignment. In short: slight wide-open softness can be normal; noticeable blur/doubling is not.