> (vascular?)

Not an expert, but from what I understood, SARS-Cov-2 infects cells through the ACE2 receptor that is present in all kinds of different cells along the blood vessels. It's "just" particularly present in the cells inside the lungs, which is why so many Covid patient could not take up enough oxygen anymore. But that somewhat nebulous "long tail" of other Covid symptoms is caused by the virus infecting other cells inside the body.

So I guess that technically makes it a vascular and not a respiratory disease.