The CD56 status of NK cells indicates the "maturity" of the cell. CD56bright NK are less effective killers but have the ability to become CD56dim when stimulated. CD56dim NK have a greater number of activating receptors on their surface, including CD16, which is the receptor that binds to antibodies. But antibody mediated killing is just one of many ways that an NK cell can target infected cells.

As far as I know, there's no evidence that the covid virus is directly recognized by NK cells. But when normal cells become infected by any virus, they start to put out distress signals that an NK cell can recognize, idenpendent of the pathogen.

I would be interested in seeing the study that found that exercise increases the proliferation of NK cells. In my experience, the portion of NK cells in an individual is fairly stable over time - it does vary widely from person to person (5-15% of white blood cells).

NK cells also have a repitior of activating receptors that fit pathogen antigens, in addition to missing-self signals. These receptors are are hardwired into our genomes to recognize the pathogens that have infected us generation after generation. Like cytomegalovirus.