So sorry to hear you are struggling. Are you recovered aside from the fatigue or still dealing with other symptoms too? Are you able to physically do any running now, how about walking? Even if you just don't have it in you to run, getting out for a walk is better than nothing and will help you keep up an exercise habit.
You have time to at least get back to where you were fitness wise even if you need some time to fully recover. You won't be starting from zero. I know people that have really pushed to keep running while recovering but personally, I think when we are dealing with illness, our body is already dedicating so much of it's resources to recovering that piling on intensive exercise can just make the whole thing take longer. That said, if your symptoms are above the shoulders (no wheezing, coughing, difficulty breathing) a little exercise can actually make nasal stuffiness feel better b/c of the vessel dilation and moving around a bit can actually give you a bit of an energy boost.
My parents caught covid last year and were hit hard with the fatigue. It took them a couple of months to not feel some level of daily fatigue. Granted, this was pre-vaccine and those I know who have been ill post-vaccine have bounced back much faster. Anyway, I know that the fatigue is hard to deal with and a looming race deadline probably isn't helping. But, YOU CAN DO IT!!
Do what you can for now and see where you stand once you are feeling better. Run/walk for the whole race is always an option too!