Leukocyte adhesion deficiency, a defect in integrin LFA1. Neutrophils are unable to adhere and migrate to infection sites, instead accumulating in blood. This explains the absence of neutrophils at infection sites and elevated neutrophils in blood.

Side note: Physeo is a great free resource with sketchy-like images to help remember immunodeficiencies and more. Not at all sponsored, just stumbled upon it during dedicated and shocked it isn't more widely known about. https://physeo.com/immunology/