The situation described in the article is very different from long haul covid. In long covid, the initial infection has passed, but its aftereffects linger. However, with long covid you aren't contagious and would almost certainly get a negative result on an antigen test.

In this situation, a severely immunocompromised patient simply can't fight off the initial infection. Where a healthy body ultimately overwhelms the virus, this patient can only kill it off partially, creating accelerated evolution since the viruses better at avoiding the weakened immune system survive. This patient could actively infect anyone at any moment (and there's a huge threat that new, dangerous strains of covid could come from a patient like this).

You know the vaccine isn’t a drug that cures active Covid infection right? It only inoculates you against contracting it.