As someone who has been treating COVID patients since early April, my working theory has been that many if not most of the secondary disease processes (non-respiratory effects of the virus), and even to some extent the worsening of respiratory function, have been largely driven by micro-thrombotic disease. Delicate capillary beds, like the ones seen in the lungs and kidneys, are highly susceptible to becoming blocked in this sort of setting. When these small vessels get plugged up, end-organ dysfunction necessarily follows. The kidney won't work properly if the blood needing filtration can't reach the nephron (functional unit of the kidney).

I'm in large part guessing here based on clinical observation, but my feeling is that you can extend this logic to other syndromes that accompany COVID-19. For example, we often see worsening liver function in the setting of this illness (albeit delayed by a few days). This could be explained in a number of ways, one of which is by impaired perfusion within capillary beds in the liver. Further, there is a myocarditis-like picture we sometimes see as well that could be explained by direct viral infection or again by impaired perfusion of the cardiac muscle by small vessel clotting.

When the thrombotic disease progresses, you start to see a more macro version: think strokes and pulmonary emboli in patients who are otherwise low risk at baseline. Thus, there's some interpolation going on here.

Hope that makes some sense.