I am definitely no expert in this area, so I will just share with you my understanding. First, I’m not familiar with using prednisone for the treatment of some of the conditions you mentioned as a standard of care, so I can’t speak to that. However, when prednisone is used for conditions such as asthma or auto-immune conditions, there is good bench research showing its affects on the immune system. I would think of endogenous prednisone as more of an immune system “regulator” than a “suppressant”. When the body gets injured, prednisone is released to regulate the immune response and healing mechanisms. You would not want the body to overactive the immune system because you would end up dieting of the strong immune response. This situation can happen in asthma attacks, sepsis and even those who died of acute Covid infection. It was the immune system which created the physiologic environment that lead to the person’s death. So, cortisol is there to tamp it down so it doesn’t over-react. In auto-immune conditions, the body is now attacking its own tissue, so suppressing the response with cortisol is helpful so the tissues have a chance to heal. Here is a paper explaining in detail what research shows about how cortisol regulates the immune response, but even this article is a little outdated.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1751559/
Hope something here addressed your thoughts.