It's probably not COVID hiding in the tissues? I wonder whether injection of genes by the virii result in altered DNA producing broken proteins. Is 23andMe data of sufficient quality to test altered DNA?
How would you look for DNA alteration, generally?
However, this is likely to be a fool's errand in this case, because this kind of sequencing normally assumes that we can take a sample of many cells from the body, and that all those cells have the exact same DNA changes. If you have a mutation that is induced in a parent or the single-figure-cell stage of embryo development then that will be true, but for DNA modification by a virus in an adult it will not be. Each cell will have a different insertion. Now, there are some techniques that can sequence the DNA from a single cell, but they don't give quite as good quality data, and because you'd be wanting to sample a good number of cells to see what the distribution of insertions is, it will likely also be very expensive.
It totally could be. Viral persistence is a strong suspect. HIV hides in "sanctuary" tissues. Other viruses and bacteria probably can evade the immune system in certain types of tissue.