I suffer from an auto-immune disease and the specific mechanism seems to involve leukocyte over-reaction, I've had COVID twice, both times unpleasant but, relative to flu, mild, and my suspicion is that COVID suppresses the immune system. That suspicion is based on the auto-immune disease stopping for a few months after COVID and my first ever flu - which was immediately following the second time I had COVID. Flu, for me at least, made COVID look like a lightweight virus. Like you I'm not willing to move beyond suspicion because of confounders.

I was vaccinated twice, very early on 2020, and auto-immune disease activity didn't reduce afterwards, while it did both times with later strains of COVID. Needs further study and really difficult to disentangle.