This is not my area but isn't the point of the mRNA vaccines that that virus' DNA is never introduced into your body? You only end up with a narrow transcribed slice of that DNA targeting a specific protein.

I've also never heard of your immune system targetting a genome; how is it generally gaining access to that genome when it is encapsulated?

My understanding of the spike targeting is that COVID is only so infectious because of the specific configuration of that spike protein. Change it too much, and it stops being nearly as infectious (and thus stops being COVID as we know it).