The real virus does not stay confined to your lungs, nor even mostly confined to your lungs
Of course not - but it is a long way from the blood and the heart.
Why do you think one of the most common first symptoms of COVID (*before* respiratory symptoms) is diarrhea?
Because mucus full of the virus goes down the throat. Epithelial spreading from top to bottom.
If the actual virus was getting to your heart muscles it's already a very serious infection, even if it is relatively asymptomatic. The lungs are the direct conduit to the bloodstream, of course, but what do you think causes the clotting? The binding of the spike protein to the ACE2 receptor. If you forgot the main point I was making, it's that the vaccine platform isn't the cause of the clotting - it's the proteins it produces that mimic the virus structure.