This is from 2 years ago, but was being discussed as early as 2020.

To be clear, McComsey isn’t suggesting that the viruses themselves are similar. Coronaviruses are not retroviruses like HIV, nor are they sexually transmitted like HIV. But it’s the way they make the people they infect sick that caught her attention. It hides in the body and continues to wreak havoc in the various organ system by driving inflammation and disrupting the immune response.

“HIV patients don’t die from the virus itself. They die from immune activation – from the high levels of inflammation that causes cancer, heart disease, liver and kidney disease,” she said.

“The only reason we cannot cure HIV is because the virus hides where the HIV drugs can’t go in. So it continues to fuel this high inflammation. That’s why somebody like me who has been studying HIV for the last 20 years found that COVID is extremely similar to HIV. It’s a virus that produces a lot of inflammation. We see a lot of conditions that are known to stem from inflammation, and now we have some evidence that it persists in different organs.” McComsey is referring to various published research papers that suggest the SARS-Cov-2 may linger in various organ tissues long after nasal swabs and blood tests come back negative.

If you wanted a more "academic" perspective, this is a study on "Long COVID" from this year.

We used ‘omic” assays and serology to deeply characterize the global and SARS-CoV-2-specific immunity in the blood of individuals with clear LC and non-LC clinical trajectories, 8 months postinfection. We found that LC individuals exhibited systemic inflammation and immune dysregulation.

This tells us that Long COVID manifests as persistent symptoms far after an acute COVID infection and appears to be, in reality, a continued infection by COVID that doesn't go away, instead hanging out in various organs and constantly challenging your immune system -- despite vaccination. Hopefully I don't need another source to tell you why this is a bad thing.